In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integra...In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.展开更多
In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integra...In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integrable equations and nonintegrable equations. By solving the （2＋1）-dimensional dispersive long wave equation, it obtains many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rationai function solutions, etc.展开更多
In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The...In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.展开更多
By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave e...By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.展开更多
The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit b...The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.展开更多
文摘In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.
基金Project supported by China Postdoctoral Science Foundation, Natural Science Foundation of Zhejiang Province of China （Grant No Y604056） and Ningbo Doctoral Foundation of China （Grant No 2005A610030）.The author would like to thank the helpful suggestions of the referee and Professor S. Y. Lou.
文摘In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integrable equations and nonintegrable equations. By solving the （2＋1）-dimensional dispersive long wave equation, it obtains many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rationai function solutions, etc.
文摘In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.
基金The project supported by China Postdoctoral Science Foundation, Natural Science Foundation of Zhejiang Province of China under Grant No. Y604056, and Doctor Foundation of Ningbo City under Grant No. 2005A610030
文摘By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the （1＋1）-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10431060, 10701011,10771009)Beijing Science Foundation of China (Grant No. 1082001)
文摘The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.
