Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 961045, 14 pages
Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms
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
Academic Editor: Y. Giga
Copyright © 2008 Bin Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 -integral model estimate method.