Exact heteroclinic breather-wave solutions for Davey-Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirota's bilinear form method and generalized ansatz method. The heteroclini...Exact heteroclinic breather-wave solutions for Davey-Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirota's bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.展开更多
The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal ...The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal or reverse order.展开更多
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi...The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.展开更多
This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone...This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone iterative method.展开更多
In this paper, the existence of the exponential attractors for the Ginzburg- Landau-BBM equations with periodic initial and boundary conditions are obtained by using the squeezing property and the operator dccompositi...In this paper, the existence of the exponential attractors for the Ginzburg- Landau-BBM equations with periodic initial and boundary conditions are obtained by using the squeezing property and the operator dccomposition method.展开更多
This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existen...This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity...The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.展开更多
This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solu...This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.展开更多
基金Supported by Chinese Natural Science Foundation under Grant No. 10661002Yunnan Natural Science Foundation under Grant No. 2006A0082M
文摘Exact heteroclinic breather-wave solutions for Davey-Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirota's bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.
基金Supported by the Education Department Foundation of Shandong Province(J07WH01)
文摘The periodic boundary value problems for nonlinear functional differential equa- tions was discussed.The existence of maximal and minimal solutions was obtained when the lower and upper solutions satisfied the formal or reverse order.
基金supported by the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences (Grant No.XDA01020304)
文摘The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.
基金Supported by Natural Science Foundation of Hainan Province(10102)
文摘This paper investigates the maximal and minimal solutions of periodic boundary value problems for second order integro-differential equations in Banach spaces by establishing a comparison result and using the monotone iterative method.
基金Supported by National Natural Science Foundation of China (19801004)
文摘In this paper, the existence of the exponential attractors for the Ginzburg- Landau-BBM equations with periodic initial and boundary conditions are obtained by using the squeezing property and the operator dccomposition method.
文摘This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.
基金supported by the National Natural Science Foundation of China(No.11201292)Shanghai Natural Science Foundation(No.12ZR1444300)the Key Discipline"Applied Mathematics"of Shanghai Second Polytechnic University(No.XXKZD1304)
文摘The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
基金supported by National Natural Science Foundation of China(Grant Nos.11431014,11371041,11401557 and 11271356)the Fundamental Research Funds for the Central Universities(Grant No.0010000048)+1 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)the Applied Mathematical Research for the Important Strategic Demand of China in Information Science and Related Fields(Grant No.2011CB808000)
文摘This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.