In this paper, based on classical Lie group method, we study multi-dimensional Landau-Lifshitz equation, and get its infinitesimal generator, symmetry group and new solutions. In particular, we build the connection be...In this paper, based on classical Lie group method, we study multi-dimensional Landau-Lifshitz equation, and get its infinitesimal generator, symmetry group and new solutions. In particular, we build the connection between new exact solutions and old exact solutions. At the same time, we also prove that the initial boundary value condition of the three-dimensional Landau-Lifshitz equation admits a unique solution and discuss the stability of the solution.展开更多
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was ...The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.展开更多
In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Li...In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.展开更多
In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solu...In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations.展开更多
In the satellite-to-ground high-speed data transmission link,there are signal self-interference problems of symbols in the co-channel,as well as between orthogonal and polarized channels.A multichannel adaptive filter...In the satellite-to-ground high-speed data transmission link,there are signal self-interference problems of symbols in the co-channel,as well as between orthogonal and polarized channels.A multichannel adaptive filter is designed by constructing a multichannel Wiener-Hopf equation,and the influence of five channel nonideal factors is suppressed to improve the BER performance.Experiments show that this method is effective to suppress the signal selfinterference,and the BER floor is optimized from 1E3 to 1E-7.展开更多
In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equatio...In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.展开更多
In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a c...In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.展开更多
A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equation...A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations. Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations. The square conserving property and the accuracy of the two methods were compared. Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.展开更多
We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimens...We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.展开更多
In this paper the generalized （3＋1）-dimensional Landau-Lifshitz equation with potential is investigated. Its exact localized and topological solutions are constructed by generalizing Hirota’s method.
We show the multidimensional stability of subsonic phase transitions in a non-isothermal van der Waals fluid. Based on the existence result of planar waves in our previous work [1], a jump condition is posed on non-is...We show the multidimensional stability of subsonic phase transitions in a non-isothermal van der Waals fluid. Based on the existence result of planar waves in our previous work [1], a jump condition is posed on non-isothermal phase boundaries which makes the argument possible. Stability of planar waves both in one dimensional and multidi-mensional spaces are proved.展开更多
This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are as...This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.展开更多
Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 ...Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.展开更多
This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi wei...This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function ω(x)=∏di=1(1-xi)^α(1+xi)^β,-1<α,β<1/d-1/2 (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approxima te solution decay exponentially. Numerical results are presen ted to demonstrate the effectiveness of the Jacobi spectral collocation method.展开更多
We consider constraint preserving multidimensional evolution equations.A prototypical example is provided by the magnetic induction equation of plasma physics.The constraint of interest is the divergence of the magnet...We consider constraint preserving multidimensional evolution equations.A prototypical example is provided by the magnetic induction equation of plasma physics.The constraint of interest is the divergence of the magnetic field.We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint.The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials.The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations.We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution,while being constraint preserving.展开更多
文摘In this paper, based on classical Lie group method, we study multi-dimensional Landau-Lifshitz equation, and get its infinitesimal generator, symmetry group and new solutions. In particular, we build the connection between new exact solutions and old exact solutions. At the same time, we also prove that the initial boundary value condition of the three-dimensional Landau-Lifshitz equation admits a unique solution and discuss the stability of the solution.
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
基金Project supported by the National Natural Science Foundation of China (No. 10471050)the Natural Science Foundation of Guangdong Province (No.031495)
文摘The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.
基金This work is partially supported by National Natural Science Foundation of China.
文摘In this paper we study the Goursat problem for semilinear hyperbolicequations with zero boundary condition where the boundary is the characteristic conefor hyperbolic operator. Our result shows that the solution is Lipschitz and is smoothaway from the characteristic cone.
文摘In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations.
基金supported by the Natural Science Foundation for Outstanding Young Scholars of Heilongjiang Province under Grant YQ2020F001the National Key Research and Development Program of China under Grant 2021YFB2900500the Fundamental Research Funds for the Central Universities under Grant FRFCU 9803503821
文摘In the satellite-to-ground high-speed data transmission link,there are signal self-interference problems of symbols in the co-channel,as well as between orthogonal and polarized channels.A multichannel adaptive filter is designed by constructing a multichannel Wiener-Hopf equation,and the influence of five channel nonideal factors is suppressed to improve the BER performance.Experiments show that this method is effective to suppress the signal selfinterference,and the BER floor is optimized from 1E3 to 1E-7.
文摘In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.
基金Project supported by the National Natural Science Foundation of China (No. 10571158)the Natural Science Foundation of Zheji-ang Province, China (No. Y605076)
文摘In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.
文摘A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations. Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations. The square conserving property and the accuracy of the two methods were compared. Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.
基金Supported by the Science Foundation of Zhejiang Sci-Tech University(No.0905828-Y)
文摘We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.
文摘In this paper the generalized （3＋1）-dimensional Landau-Lifshitz equation with potential is investigated. Its exact localized and topological solutions are constructed by generalizing Hirota’s method.
文摘We show the multidimensional stability of subsonic phase transitions in a non-isothermal van der Waals fluid. Based on the existence result of planar waves in our previous work [1], a jump condition is posed on non-isothermal phase boundaries which makes the argument possible. Stability of planar waves both in one dimensional and multidi-mensional spaces are proved.
基金supported by National Natural Science Foundation of China(Grant Nos.11031003,11271172 and 11071105)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2014063)+2 种基金China Postdoctoral Science Foundation Funded Project(Grant No.2012M520716)Heilongjiang Postdoctoral Fund(Grant No.LBH-Z12135)New Century Excellent Talents in University(Grant No.NCET-10-0470)
文摘This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
文摘Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type:{-dY t = f(t1, Y t1 , Z t1 , Y t+δ(t) , Z t+ζ(t) )dt Z t dB t1 , t ∈ [0, T ], Y t = ξ t1 , t ∈ [T, T + K], Z t = η t1 , t ∈ [T, T + K].In this paper, we give a necessary and sufficient condition under which the comparison theorem holds for multidimensional anticipated backward stochastic differential equations with generators independent of the anticipated term of Z.
基金the National Natural Science Foundation of China (Grant Nos. 11671157, 11826212).
文摘This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function ω(x)=∏di=1(1-xi)^α(1+xi)^β,-1<α,β<1/d-1/2 (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approxima te solution decay exponentially. Numerical results are presen ted to demonstrate the effectiveness of the Jacobi spectral collocation method.
基金E.Tadmor Research was supported in part by NSF grant 07-07949 and ONR grant N00014-091-0385.
文摘We consider constraint preserving multidimensional evolution equations.A prototypical example is provided by the magnetic induction equation of plasma physics.The constraint of interest is the divergence of the magnetic field.We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint.The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials.The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations.We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution,while being constraint preserving.
