Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Existence and Extinction of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Terms | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 961045 14 pages doi 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 Correspondence should be addressed to Bin Wu wubing790831@ Received 2 March 2008 Accepted 13 August 2008 Recommended by Y. Giga 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. 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. 1. Introduction The scaled semiconductor drift-diffusion model reads -V- V p - n C x nt- Jn r n p 1 - np g Jn V nm - nVỳ pt Jp r n p 1 - np g -Jp V pm pVỳ with x e Q c RN which denotes the bounded domain occupied by semiconductor crystal. Here the unknowns y n and p denote the electrostatic potential the electron density and the hole density respectively. The Jn represents the electron current and Jp is the analogously defined physical quantity of the positively charged holes. Additionally the given function C x denotes the doping profile fixed charged background ions characterizing the semiconductor under consideration R n p r n p 1 - np the net recombinationgeneration rate and g
