In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i...Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.展开更多
We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles inst...We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.展开更多
A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordin...A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.展开更多
Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation a...Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.展开更多
In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process in a Ranque-Hi...Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process in a Ranque-Hilsch vortex tube cleaning （cooling） system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-c turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows in the air separators. Results present a comprehensive and practical solution for use in future numerical studies.展开更多
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classificati...This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.展开更多
This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k ...This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].展开更多
This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-w...This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-where Ω∈R N is a bounded domain with smooth boundary Ω,m,n,p are positive constants, γ is the outward normal vector. The necessary and sufficient conditions for the global existence of solutions are obtained.展开更多
Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of ...Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of the simulation indicate that the WBC is prone to penetrating into the gap under northerly winds, and its path is more difficult to alter due to the larger interval between the two critical transition curves (C1P and C1L). For southerly winds, the WBC is prone to leaping across the gap, and its path is easier to alter due to the smaller interval between the two critical transition curves. The simulation results also indicate that the meridional winds over the southern region of the gap are the dominant factor determining the formation of the WBC. The dynamic mechanism influencing the transport of WBC near the gap is both Ekman transport and the blocking of Ekman transport. Ekman transport induced by northerly winds may reduce the transport of the WBC, causing the β-effect to dominate the meridional advection (promoting the penetration). Southerly winds, however, may enhance the transport of the WBC, causing the meridional advection to dominate the β-effect (promoting the leaping state). These results explain some structural features of the Kuroshio at the Luzon Strait.展开更多
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions...The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.展开更多
In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general in...In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.展开更多
A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented.The electro-magnetic,mechanical and fluid subsystems of the valve were investigated,including their interactions.Governing equation...A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented.The electro-magnetic,mechanical and fluid subsystems of the valve were investigated,including their interactions.Governing equations of the valve were derived in the form of nonlinear state equations.By comparing the simulated and measured data,the simulation model is validated with a deviation less than 15%,which can be used for the structural design and control algorithm optimization of proportional solenoid valves.展开更多
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
文摘Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.
基金supported by National Natural Science Foundation of China under Grant No.60674062the Middle-Aged and Young Scientists Research Incentive Fund of Shandong Province under Grant No.2007BS01013
文摘We analyze a new car-following model described by a differential-difference equation with a synthesized optimal velocity function (SOVF),which depends on the front interactions between every two adjacent vehicles instead of the weighted average headway.The model is analyzed with the use of the linear stability theory and nonlinear analysis method.The stability and neutral stability condition are obtained.We also derive the modified KdV (Korteweg-de Vries) equation and the kink-antikink soliton solution near the critical point.A simulation is conducted with integrating the differential-difference equation by the Euler scheme.The results of the numerical simulation verify the validity of the new model.
基金The National Natural Science Foundation of China (No10471023)
文摘A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.
文摘Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
文摘Air separators provide safe, clean, and appropriate air flow to engines and are widely used in vehicles with large engines such as ships and submarines. In this operational study, the separation process in a Ranque-Hilsch vortex tube cleaning （cooling） system is investigated to analyze the impact of the operating gas type on the vortex tube performance; the operating gases used are air, nitrogen, oxygen, carbon dioxide and nitrogen dioxide. The computational fluid dynamic model used is equipped with a three-dimensional structure, and the steady-state condition is applied during computations. The standard k-c turbulence model is employed to resolve nonlinear flow equations, and various key parameters, such as hot and cold exhaust thermal drops, and power separation rates, are described numerically. The results show that nitrogen dioxide creates the greatest separation power out of all gases tested, and the numerical results are validated by good agreement with available experimental data. In addition, a comparison is made between the use of two different boundary conditions, the pressure-far-field and the pressure-outlet, when analyzing complex turbulent flows in the air separators. Results present a comprehensive and practical solution for use in future numerical studies.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.
文摘This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].
文摘This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations:u t=1m△u m-u n, x∈Ω,t>0 1m·u mv=u p,x∈Ω,t>0 u(x,0)=u 0(x)>0,x∈Ω-where Ω∈R N is a bounded domain with smooth boundary Ω,m,n,p are positive constants, γ is the outward normal vector. The necessary and sufficient conditions for the global existence of solutions are obtained.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (Nos. KZCX1-YW-12, KZCX2-YW-201)the National Natural Science Foundation of China (No. 90411013)+2 种基金the National Basic Research Program of China (973 Program, No. 2006CB403600)NSFC's Outstanding Youth Grant (No. 40888001)the 100-Talent Program of the CAS, and the Outstanding Youth Grant of Shandong Province
文摘Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of the simulation indicate that the WBC is prone to penetrating into the gap under northerly winds, and its path is more difficult to alter due to the larger interval between the two critical transition curves (C1P and C1L). For southerly winds, the WBC is prone to leaping across the gap, and its path is easier to alter due to the smaller interval between the two critical transition curves. The simulation results also indicate that the meridional winds over the southern region of the gap are the dominant factor determining the formation of the WBC. The dynamic mechanism influencing the transport of WBC near the gap is both Ekman transport and the blocking of Ekman transport. Ekman transport induced by northerly winds may reduce the transport of the WBC, causing the β-effect to dominate the meridional advection (promoting the penetration). Southerly winds, however, may enhance the transport of the WBC, causing the meridional advection to dominate the β-effect (promoting the leaping state). These results explain some structural features of the Kuroshio at the Luzon Strait.
基金The project supported by the Natural Science Foundation of Shandong Province and the Natural Science Foundation of Liaocheng University
文摘The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
文摘In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance.
基金Project(2008ZHZX1A0502) supported by the Independence Innovation Achievements Transformation Crucial Special Program of Shandong Province,China
文摘A multi-domain nonlinear dynamic model of a proportional solenoid valve was presented.The electro-magnetic,mechanical and fluid subsystems of the valve were investigated,including their interactions.Governing equations of the valve were derived in the form of nonlinear state equations.By comparing the simulated and measured data,the simulation model is validated with a deviation less than 15%,which can be used for the structural design and control algorithm optimization of proportional solenoid valves.
