A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.
In this paper, a networked control problem is addressed for a class of singular systems with time-varying tran...
Wang Yanyan 1 , Wang Zhiming 2 , Ni Mingkang 2 , Liu Wei 1, 2 1. Department of Mathematics, Zhoukou Normal University, Henan, 466001, China2. Center for Applied and Multidisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai, 200241, China
In this paper,we address the existence and asymptotic analysis of higher-dimensional contrast structure of singularly perturbed Dirichlet problem.Based on the existence,an asymptotical analysis of a steplike contrast structure (i.e.,an internal transition layer solution) is studied by the boundary function method via a proposed smooth connection.In the framework of this paper,we propose a first integral condition,under which the existence of a heteroclinic orbit connecting two equilibrium points is ensured in a higher-dimensional fast phase space.Then,the step-like contrast structure is constructed,and the internal transition time is determined.Meanwhile,the uniformly valid asymptotical expansion of such an available step-like contrast structure is obtained.Finally,an example is presented to illustrate the result.