We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min...We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.展开更多
In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a ste...In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.展开更多
In the literature,stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following two conditions：（1） The considered isochrone and the target reflector are tangential to each ...In the literature,stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following two conditions：（1） The considered isochrone and the target reflector are tangential to each other;（2） The spatial duration of the wavelet of the depthmigrated image is short.For the isochrones that are not tangential to the target reflector and for the depth-migrated images that have a large spatial duration,the published stationary phase equation for the demigrated field will become invalid.For performing the stationary phase analysis of the Kirchhoff-type demigrated field under the conditions that the considered isochrone and the target reflector are not tangential to each other and that the spatial duration of the wavelet of the depth-migrated image is not short（the general conditions）,I derive the formulas for the factors appearing in the stationary phase formula in two dimensions,from which I find that for different isochrones the horizontal coordinates of the stationary point of the depth difference function are different.Also,the equation for the Kirchhoff-type demigrated field consists of two parts.One is the true-amplitude demigrated signal and the other is the amplitude distortion factor.From these facts the following two conclusions can be drawn：（1） A demigrated signal is composed of many depth-migrated images and one depth-migrated image trace provides only one sample to the demigrated signal;and（2） The amplitude distortion effect is an effect inherent in the Kirchhoff-type demigration and cannot be eliminated during demigration.If this effect should be eliminated,one should do an amplitude correction after demigration.展开更多
This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dim...This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.展开更多
This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausd...This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.展开更多
In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the exis...In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.展开更多
In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial m...In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.展开更多
This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global ex...This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global existence of solutions by constructing a stable set in and show the energy exponential decay estimate by applying a lemma of V. Komornik.展开更多
Demigration refers to directly applying a specific imaging technique to a migrated section. It is applied primarily to seismic data mapping. In a previous research study, a time-efficient implementation technology of ...Demigration refers to directly applying a specific imaging technique to a migrated section. It is applied primarily to seismic data mapping. In a previous research study, a time-efficient implementation technology of demigration was expounded. In the present study, the Fast Marching Method （FMM） used for traveltime computation in the isochrone-staek demigration, is developed. Furthermore, other key techniques （ such as selection of aperture and antialiasing filtering factor） are analyzed in detail. Besides, the detail implementation method and program flow are given, which is shown their good computational efficiency and high-quality demi- gration effect. This implementation technique is illustrated with both the V（z） model and Marmousi model. It provides a basic method for implementing demigration in the application of seismic data mapping.展开更多
This paper introduces an internal multiple prediction method based on imaging profile prediction and Kirchhoff demigration.First,based on an inputted prestack time migration profile,the method predicts the prestack ti...This paper introduces an internal multiple prediction method based on imaging profile prediction and Kirchhoff demigration.First,based on an inputted prestack time migration profile,the method predicts the prestack time migration profile that only includes internal multiples by inverse scattering series method.Second,the method uses velocity-weighted Kirchhoff demigration to create shot gathers that contains only internal multiples.Internal multiple prediction based on the prestack time migration profile effectively reduces the computational cost of multiple predictions,and the internal-multiple shot gathers created by Kirchhoff demigration remarkably reduces the complexity of the practical problem.Internal multiple elimination can be conducted through the combined adaptive multiple subtraction based on event tracing.Synthetic and field data tests show that the method effectively predicts internal multiples and possesses considerable potential in field data processing,particularly in areas where internal multiples develop seriously.展开更多
In this paper, we study the existence of nodal solutions of the following general Schödinger-Kirchhoff type problem: where a,b > 0, N ≥ 3, g : R → R+ is an even differential function and g''(s) ...In this paper, we study the existence of nodal solutions of the following general Schödinger-Kirchhoff type problem: where a,b > 0, N ≥ 3, g : R → R+ is an even differential function and g''(s) ≥ 0 for all s ≥ 0, h : R → R is an odd differential function. These equations are related to the generalized quasilinear Schödinger equations: Because the general Schödinger-Kirchhoff type problem contains the nonlocal term, it implies that the equation (KP1) is no longer a pointwise identity and is very different from classical elliptic equations. By introducing a variable replacement, we first prove that (KP1) is equivalent to the following problem: whereand G-1 is the inverse of G. Next, we prove that (KP2) is equivalent to the following system with respect to : For every integer k > 0, radial solutions of (KP1) with exactly k nodes are obtained by dealing with the system (S) under some appropriate assumptions. Moreover, this paper established the nonexistence results if N ≥ 4 and b is sufficiently large.展开更多
Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We ...Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We prove the existence and uniqueness of global solutions under non-linear boundary conditions which the model is added one damping mechanism at l end. What is more, we also prove the exponential decay property of the energy of above mentioned system.展开更多
The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method...The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition.展开更多
In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is...In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.展开更多
.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of....In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.展开更多
文摘We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.
基金the National Natural Science Foundation of China (11971393)。
文摘In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.
基金supported by the National Natural Science Foundation of China (Grant No.40574052)
文摘In the literature,stationary phase analysis of Kirchhoff-type demigrated fields is carried out mainly under the following two conditions：（1） The considered isochrone and the target reflector are tangential to each other;（2） The spatial duration of the wavelet of the depthmigrated image is short.For the isochrones that are not tangential to the target reflector and for the depth-migrated images that have a large spatial duration,the published stationary phase equation for the demigrated field will become invalid.For performing the stationary phase analysis of the Kirchhoff-type demigrated field under the conditions that the considered isochrone and the target reflector are not tangential to each other and that the spatial duration of the wavelet of the depth-migrated image is not short（the general conditions）,I derive the formulas for the factors appearing in the stationary phase formula in two dimensions,from which I find that for different isochrones the horizontal coordinates of the stationary point of the depth difference function are different.Also,the equation for the Kirchhoff-type demigrated field consists of two parts.One is the true-amplitude demigrated signal and the other is the amplitude distortion factor.From these facts the following two conclusions can be drawn：（1） A demigrated signal is composed of many depth-migrated images and one depth-migrated image trace provides only one sample to the demigrated signal;and（2） The amplitude distortion effect is an effect inherent in the Kirchhoff-type demigration and cannot be eliminated during demigration.If this effect should be eliminated,one should do an amplitude correction after demigration.
文摘This paper deals with the Hausdorff dimensions of the global attractor for a class of Kirchhoff-type coupled equations with strong damping and source terms. We obtain a precise estimate of upper bound of Hausdorff dimension of the global attractor.
文摘This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.
文摘In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.
文摘In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2.
文摘This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms in a bounded domain, where and are constants. We obtain the global existence of solutions by constructing a stable set in and show the energy exponential decay estimate by applying a lemma of V. Komornik.
基金Supported by the National Natural Science Foundation of China(No.41274120)
文摘Demigration refers to directly applying a specific imaging technique to a migrated section. It is applied primarily to seismic data mapping. In a previous research study, a time-efficient implementation technology of demigration was expounded. In the present study, the Fast Marching Method （FMM） used for traveltime computation in the isochrone-staek demigration, is developed. Furthermore, other key techniques （ such as selection of aperture and antialiasing filtering factor） are analyzed in detail. Besides, the detail implementation method and program flow are given, which is shown their good computational efficiency and high-quality demi- gration effect. This implementation technique is illustrated with both the V（z） model and Marmousi model. It provides a basic method for implementing demigration in the application of seismic data mapping.
基金support of the NSFC-Shandong Joint Fund for Marine Science Research Centers (No. U1606401)the National Natural Science Foundation of China (Nos. 41704114 and 41574105)+3 种基金the National Science and Technology Major Project of China (No. 2016Z X05027-002)the Scientific and Technological Innovation Project financially supported by Qingdao National Laboratory for Marine Science and Technology (No. 2016 ASKJ13)Taishan Scholar Project Funding (No. tspd2016 1007)the Latitudinal Project of Algorithm Research of Internal Multiple Prediction financially supported by CNOOC
文摘This paper introduces an internal multiple prediction method based on imaging profile prediction and Kirchhoff demigration.First,based on an inputted prestack time migration profile,the method predicts the prestack time migration profile that only includes internal multiples by inverse scattering series method.Second,the method uses velocity-weighted Kirchhoff demigration to create shot gathers that contains only internal multiples.Internal multiple prediction based on the prestack time migration profile effectively reduces the computational cost of multiple predictions,and the internal-multiple shot gathers created by Kirchhoff demigration remarkably reduces the complexity of the practical problem.Internal multiple elimination can be conducted through the combined adaptive multiple subtraction based on event tracing.Synthetic and field data tests show that the method effectively predicts internal multiples and possesses considerable potential in field data processing,particularly in areas where internal multiples develop seriously.
文摘In this paper, we study the existence of nodal solutions of the following general Schödinger-Kirchhoff type problem: where a,b > 0, N ≥ 3, g : R → R+ is an even differential function and g''(s) ≥ 0 for all s ≥ 0, h : R → R is an odd differential function. These equations are related to the generalized quasilinear Schödinger equations: Because the general Schödinger-Kirchhoff type problem contains the nonlocal term, it implies that the equation (KP1) is no longer a pointwise identity and is very different from classical elliptic equations. By introducing a variable replacement, we first prove that (KP1) is equivalent to the following problem: whereand G-1 is the inverse of G. Next, we prove that (KP2) is equivalent to the following system with respect to : For every integer k > 0, radial solutions of (KP1) with exactly k nodes are obtained by dealing with the system (S) under some appropriate assumptions. Moreover, this paper established the nonexistence results if N ≥ 4 and b is sufficiently large.
文摘Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We prove the existence and uniqueness of global solutions under non-linear boundary conditions which the model is added one damping mechanism at l end. What is more, we also prove the exponential decay property of the energy of above mentioned system.
文摘The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition.
基金supported by the National Natural Science Foundation of China(No.62175100)Spark Program of Earthquake Sciences of CEA(No.XH22015A)+1 种基金Henan Province Seismic Structure Exploration project(YCZC-2020-950)Special Fund of Chinese Central Government for Basic Scientific Research Operations in Commonweal Research Institutes(No.IGCEA1902)。
基金supported in part by the National Key Research and Development Program(2021YFF1500100)Key Basic Research of Basic Strengthening Program of the Science and Technology Commission(2020-JCJQ-ZD-068)。
文摘In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.
文摘.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.
