Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 961045, 14 pages
doi:10.1155/2008/961045
Research Article

Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms

Bin Wu

 Department of Information and Computing Sciences, College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China
Received 2 March 2008; Accepted 13 August 2008

Recommended by Y. Giga

Abstract

We consider the transient drift-diffusion model with fast diffusion terms. This problem is not only degenerate but also singular. We first present existence result for general nonlinear diffusivities for the Dirichlet-Neumann mixed boundary value problem. Then, the extinction phenomenon of weak solutions for the homogeneous Dirichlet boundary problem is studied. Sufficient conditions on the extinction and decay estimates of solutions are obtained by using Lp-integral model estimate method.