A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the tra...A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.展开更多
The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and em...The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ +∞.展开更多
A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into account nonlinear rheology, a semi-empirical rheological model is applied to this water-mu...A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into account nonlinear rheology, a semi-empirical rheological model is applied to this water-mud model, reflecting the combined visco-elasto-plastic properties of soft mud under such oscillatory external forces as water waves. In order to increase the resolution of the flow in the neighborhood of both sides of the inter-surface, a logarithmic grid in the vertical direction is employed for numerical treatment. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.展开更多
This paper aims to numerically investigate the impact of the combination of groynes and vertical piers on mitigating the amplitude and celerity of dam break wave-front.First,a robust numerical model based on the Finit...This paper aims to numerically investigate the impact of the combination of groynes and vertical piers on mitigating the amplitude and celerity of dam break wave-front.First,a robust numerical model based on the Finite Volume Method(FVM)with the Harten,Lax and van Leer(HLL)approximate Reimann’s solver’s technique is developed and validated with other research studies.Then many different scenarios including group of piers,group of groynes with different shapes and combination of groynes and piers are considered for dam break flow modeling.The final results showed that group of piers alone or group of groynes alone have no significant effects on the wave-front depth and celerity but,combination of L-head groyne with piers can decrease the amplitude and celerity of the dam break wavefront or flood wave.In this case,a blockage zone between the groynes and intensive backwater effects behind them were observed.展开更多
A numerical solution was derived to determine wave field in a converging channel bounded by rubble-mound jetties. The solution was achieved by applying boundary element method. The model was applied to analyze the eff...A numerical solution was derived to determine wave field in a converging channel bounded by rubble-mound jetties. The solution was achieved by applying boundary element method. The model was applied to analyze the effect of channel convergence, the cross-section of the jetties and their physical and damping properties on wave field in the channel. The study reveals numerous non-intuitive results specific for jetted and convergent channels. The analysis shows that wave reflection is usually low and is of secondary practical importance. Wave transmission strongly depends on the channel geometry and transmitted waves may be higher than incident waves, despite reflection and damping processes. Moreover, wave transmission depends on physical and damping properties of rubble jetties and the results show that wave transmission may increase with the increasing damping properties of jetties, which is a non-intuitive feature of wave fields in jetted channels. The analysis reveals several novel results of practical importance. It is shown that the rubble-mound jetties should be constructed from the material of high porosity, which ensures low transmission. More attention should be devoted to hydraulic properties of porous materials. It is recommended to use the material of moderate damping properties. The material of high damping properties often increases the wave transmission. It is possible, by a selection of rubble-mound material, to obtain lower transmission level for steep waves than for waves of moderate steepness. A series of laboratory experiments were conducted in the wave flume to verify the theoretical results. The comparisons show that theoretical results are in fairly good agreement with experimental data.展开更多
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t 〉 0, x = (x...This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t 〉 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) 〈 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.展开更多
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt +ut = uxx -V′(u) on R. The long-time asymptotics of the solutions of this equation are quite similar t...The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt +ut = uxx -V′(u) on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx - V′(u). Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V, the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.展开更多
In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally...In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p (2 ≤ p ≤ ∞) decay estimates of the solution.展开更多
Data from spacecrafts suggest that space plasma has an abundance of suprathermal particles which are controlled by the spectral index κ when modeled on kappa particle velocity distribution. In this paper, considering...Data from spacecrafts suggest that space plasma has an abundance of suprathermal particles which are controlled by the spectral index κ when modeled on kappa particle velocity distribution. In this paper, considering homogeneous plasma, the effect of integer values of κ on the damping rate of an obliquely propagating magnetosonic(MS) wave is studied. The frequency of the MS wave is assumed to be less than ion cyclotron frequency, i.e.,iw(28)w. Under this assumption, the dispersion relation is investigated both numerically and analytically, and it is found that the real frequency of the wave is not a sensitive function of κ, but the imaginary part of the frequency is. It is also shown that for those values of κ where a large number of resonant particles participate in wave–particle interaction, the wave is heavily damped, as expected. The possible application of the results to the solar wind is discussed.展开更多
The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u+b(t)ut=f(u),u(0,χ)=u0(χ),ut(0,χ)=u1(χ) in any space dimension n ≥ 1. It is assumed that the time-dependent dampin...The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u+b(t)ut=f(u),u(0,χ)=u0(χ),ut(0,χ)=u1(χ) in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b(t)〉 0 is effective, and in particular tb(t) →∞ as t →∞. The global existence of small energy data solutions for|f(u)|≈|u|^p in the supercritical case of p 〉 1+ 2/n and p ≤n/n-2 for n ≥ 3 is proved.展开更多
Abstract This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+{utt-txx+ut+f(u)x=0,t〉0,x∈R+,u(0,x)=u0(x)→u+,asx→...Abstract This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+{utt-txx+ut+f(u)x=0,t〉0,x∈R+,u(0,x)=u0(x)→u+,asx→+∞,ut(0,x)=u1(x),u(t,0)=ub.For the non-degenerate case f](u+) 〈 0, it is shown in [1] that the above initialboundary value problem admits a unique global solution u(t,x) which converges to the stationary wave φ(x) uniformly in x ∈ R+ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. Moreover, by using the space-time weighted energy method initiated by Kawashima and Matsumura [2], the convergence rates (including the algebraic convergence rate and the exponential convergence rate) of u(t, x) toward φ(x) are also obtained in [1]. We note, however, that the analysis in [1] relies heavily on the assumption that f'(ub) 〈 0. The main purpose of this paper is devoted to discussing the case of f'(ub)= 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.展开更多
The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The re...A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model(ε) and that devised for the modified potential flow model(μ_p) is established, namely, μ_p=3πεω_n/8 (where ω_n is the natural frequency). This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.展开更多
Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation ...Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.展开更多
In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ...In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ■R^3 is a smooth bounded domain,in H^10(Ω)×L^2(Ω)is in fact bounded in D(B0)×H^10(Ω)As an application of our results,we obtain the upper-semicontinuity for global attractor of the weakly damped semilinear wave equation in the norm of H^1(Ω)×L^2(Ω)when the interior variable damping converges to theboundary damping in the sense of distributions.展开更多
In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter cond...In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.展开更多
The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly d...The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.展开更多
Based on the damped wave equation,the damped wave equation for seismic exploration is given for the study on evaluation problem of stratum acoustic impedance by the seismic data records.And applying Cauchy Problem ins...Based on the damped wave equation,the damped wave equation for seismic exploration is given for the study on evaluation problem of stratum acoustic impedance by the seismic data records.And applying Cauchy Problem instead of mixed problem in the process Of identifying acoustic impedance,we for give a fast identification algorithm of recurtive layer by layer.In order to avoid the accumulation of errors while identifying,the method of removing errors layer by layer is taken.So using the principle of Pulse Variation and even under the circumstance of big noise,we can identify the structure of stratum clearly.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10972117)
文摘A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.
基金supported by National Natural Science Foundation of China(Nos.91026005,11275156,11047010,61162017)
文摘The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ +∞.
文摘A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into account nonlinear rheology, a semi-empirical rheological model is applied to this water-mud model, reflecting the combined visco-elasto-plastic properties of soft mud under such oscillatory external forces as water waves. In order to increase the resolution of the flow in the neighborhood of both sides of the inter-surface, a logarithmic grid in the vertical direction is employed for numerical treatment. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.
基金supported by the“National Major Science and Technology Program for Water Pollution Control and Treatment”(2017ZX07101001)“Chinese National Natural Science Foundation”(No.41871072)“Young Scientists Exchange Program(TYSP)”(Grant nos.Iran-18-008 and Iran-18-009)。
文摘This paper aims to numerically investigate the impact of the combination of groynes and vertical piers on mitigating the amplitude and celerity of dam break wave-front.First,a robust numerical model based on the Finite Volume Method(FVM)with the Harten,Lax and van Leer(HLL)approximate Reimann’s solver’s technique is developed and validated with other research studies.Then many different scenarios including group of piers,group of groynes with different shapes and combination of groynes and piers are considered for dam break flow modeling.The final results showed that group of piers alone or group of groynes alone have no significant effects on the wave-front depth and celerity but,combination of L-head groyne with piers can decrease the amplitude and celerity of the dam break wavefront or flood wave.In this case,a blockage zone between the groynes and intensive backwater effects behind them were observed.
文摘A numerical solution was derived to determine wave field in a converging channel bounded by rubble-mound jetties. The solution was achieved by applying boundary element method. The model was applied to analyze the effect of channel convergence, the cross-section of the jetties and their physical and damping properties on wave field in the channel. The study reveals numerous non-intuitive results specific for jetted and convergent channels. The analysis shows that wave reflection is usually low and is of secondary practical importance. Wave transmission strongly depends on the channel geometry and transmitted waves may be higher than incident waves, despite reflection and damping processes. Moreover, wave transmission depends on physical and damping properties of rubble jetties and the results show that wave transmission may increase with the increasing damping properties of jetties, which is a non-intuitive feature of wave fields in jetted channels. The analysis reveals several novel results of practical importance. It is shown that the rubble-mound jetties should be constructed from the material of high porosity, which ensures low transmission. More attention should be devoted to hydraulic properties of porous materials. It is recommended to use the material of moderate damping properties. The material of high damping properties often increases the wave transmission. It is possible, by a selection of rubble-mound material, to obtain lower transmission level for steep waves than for waves of moderate steepness. A series of laboratory experiments were conducted in the wave flume to verify the theoretical results. The comparisons show that theoretical results are in fairly good agreement with experimental data.
基金The research of Fan Lili was supported by two grants from the National Natural Science Foundation of China (10871151 10925103)+1 种基金the research of Liu Hongxia was supported by National Natural Science Foundation of China (10871082)the research of Yin Hui was supported by National Natural Sciences Foundation of China (10901064)
文摘This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t 〉 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) 〈 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.
文摘The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt +ut = uxx -V′(u) on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx - V′(u). Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V, the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.
基金supported by Shanghai Municipal Natural Science Foundation 09ZR1413500National Natural Science Foundation of China 11071162
文摘In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p (2 ≤ p ≤ ∞) decay estimates of the solution.
文摘Data from spacecrafts suggest that space plasma has an abundance of suprathermal particles which are controlled by the spectral index κ when modeled on kappa particle velocity distribution. In this paper, considering homogeneous plasma, the effect of integer values of κ on the damping rate of an obliquely propagating magnetosonic(MS) wave is studied. The frequency of the MS wave is assumed to be less than ion cyclotron frequency, i.e.,iw(28)w. Under this assumption, the dispersion relation is investigated both numerically and analytically, and it is found that the real frequency of the wave is not a sensitive function of κ, but the imaginary part of the frequency is. It is also shown that for those values of κ where a large number of resonant particles participate in wave–particle interaction, the wave is heavily damped, as expected. The possible application of the results to the solar wind is discussed.
基金Project supported by a grant of DFG (Deutsche Forschungsgemeinschaft) for the research project "Influence of time-dependent coefficients on semi-linear wave models" (No. RE 961/17-1)
文摘The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u+b(t)ut=f(u),u(0,χ)=u0(χ),ut(0,χ)=u1(χ) in any space dimension n ≥ 1. It is assumed that the time-dependent damping term b(t)〉 0 is effective, and in particular tb(t) →∞ as t →∞. The global existence of small energy data solutions for|f(u)|≈|u|^p in the supercritical case of p 〉 1+ 2/n and p ≤n/n-2 for n ≥ 3 is proved.
基金This work was supported by two grants from the National Natural Science Foundation of China under contracts 10431060 and 10329101 respectively.
文摘Abstract This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+{utt-txx+ut+f(u)x=0,t〉0,x∈R+,u(0,x)=u0(x)→u+,asx→+∞,ut(0,x)=u1(x),u(t,0)=ub.For the non-degenerate case f](u+) 〈 0, it is shown in [1] that the above initialboundary value problem admits a unique global solution u(t,x) which converges to the stationary wave φ(x) uniformly in x ∈ R+ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. Moreover, by using the space-time weighted energy method initiated by Kawashima and Matsumura [2], the convergence rates (including the algebraic convergence rate and the exponential convergence rate) of u(t, x) toward φ(x) are also obtained in [1]. We note, however, that the analysis in [1] relies heavily on the assumption that f'(ub) 〈 0. The main purpose of this paper is devoted to discussing the case of f'(ub)= 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.
基金supported by the National Science Foundation of China under Grant Nos.60225003,60334040,60221301,60774025,10831007,61104129,11171195the Excellent PhD Adviser Program of Beijing under Grant No.YB20098000101
文摘The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51490673,51479025 and 51279029)
文摘A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model(ε) and that devised for the modified potential flow model(μ_p) is established, namely, μ_p=3πεω_n/8 (where ω_n is the natural frequency). This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.
基金supported by National Natural Science Foundation of China(Grant Nos.11201103 and 11471288)supported by the China Scholarship Council
文摘Instead of the L^p estimates,we study the modulation space estimates for the solution to the damped wave equation.Decay properties for both the linear and semilinear equations are obtained.The estimates in modulation space differ in many aspects from those in L^p space.
基金The first author is supported by“the Fundamental Research Funds for the Central Universities”,NO.NS2020058was supported by the National Natural Science Foundation of China under Grant 11501289.
文摘In this paper we prove that every compact invariant subset■associated with the semigroup{Sn,k(t)}t≥0 generated by wave equations with variable damping,either in the interior or on the boundary of the domainΩwhereΩ■R^3 is a smooth bounded domain,in H^10(Ω)×L^2(Ω)is in fact bounded in D(B0)×H^10(Ω)As an application of our results,we obtain the upper-semicontinuity for global attractor of the weakly damped semilinear wave equation in the norm of H^1(Ω)×L^2(Ω)when the interior variable damping converges to theboundary damping in the sense of distributions.
基金supported by Shanghai Leading Academic Discipline Project (No. S30501)Shanghai Natural Science Foundation Project (No. 10ZR1420800)
文摘In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.
基金supported in part by NSF of China,N.10771142the National Basic Research Project of China,N.2005CB321701+2 种基金Shuguang Project of Shanghai Education Commission,N.08SG45Shanghai Leading Academic Discipline Project N.S30405The Fund for E-institute of Shanghai Universities N.E03004.
文摘The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.
文摘Based on the damped wave equation,the damped wave equation for seismic exploration is given for the study on evaluation problem of stratum acoustic impedance by the seismic data records.And applying Cauchy Problem instead of mixed problem in the process Of identifying acoustic impedance,we for give a fast identification algorithm of recurtive layer by layer.In order to avoid the accumulation of errors while identifying,the method of removing errors layer by layer is taken.So using the principle of Pulse Variation and even under the circumstance of big noise,we can identify the structure of stratum clearly.