Open Access

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

Journal of Inequalities and Applications20082008:961045

https://doi.org/10.1155/2008/961045

Received: 2 March 2008

Accepted: 13 August 2008

Published: 14 August 2008

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 -integral model estimate method.

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Authors’ Affiliations

(1)
Department of Information and Computing Sciences, College of Mathematics and Physics, Nanjing University of Information Science and Technology

Copyright

© BinWu. 2008

This article is published under license to BioMed Central Ltd. 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.