The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the probl...The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.展开更多
This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are d...This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.展开更多
In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis ...In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis set,by which physical quantities are approximated with their values and derivatives associated with grid points.Nonlinear operations on functions are carried out in the framework of differential algebra.Then,by introducing scalar products and requiring the residue to be orthogonal to the basis,the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives.The method gives stable,less diffusive,and accurate results for the CNLS equations.展开更多
文摘The initial boundary value problems for a class of high order Kirchhoff type equations with nonlinear strongly damped terms are considered. We establish the existence and uniqueness of the global solution of the problem by using prior estimates and Galerkin’s method under proper assumptions for the rigid term. Then the compact method is used to prove the existence of a compact family of global attractors in the solution semigroup generated by the problem. Finally, the Frechet differentiability of the operator semigroup and the decay of the volume element of linearization problem are proved, and the Hausdorff dimension and Fractal dimension of the family of global attractors are obtained.
基金supported by the National Natural Science Foundation of China (No. 10572049)
文摘This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness ratio, and length-to-width ratio.
文摘In this paper,we present solutions for the one-dimensional coupled nonlinear Schrödinger(CNLS)equations by the Constrained Interpolation Profile-Basis Set(CIP-BS)method.This method uses a simple polynomial basis set,by which physical quantities are approximated with their values and derivatives associated with grid points.Nonlinear operations on functions are carried out in the framework of differential algebra.Then,by introducing scalar products and requiring the residue to be orthogonal to the basis,the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives.The method gives stable,less diffusive,and accurate results for the CNLS equations.
