TAILIEUCHUNG - Báo cáo sinh học: " Research Article Quenching for a Reaction-Diffusion System with Coupled Inner Singular Absorption Terms Shouming Zhou and Chunlai Mu"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Quenching for a Reaction-Diffusion System with Coupled Inner Singular Absorption Terms Shouming Zhou and Chunlai Mu | Hindawi Publishing Corporation Boundary Value Problems Volume 2o10 Article ID 797182 15 pages doi 2010 797182 Research Article Quenching for a Reaction-Diffusion System with Coupled Inner Singular Absorption Terms Shouming Zhou and Chunlai Mu College of Mathematics and Statistics Chongqing University Chongqing 400044 China Correspondence should be addressed to Shouming Zhou zhoushouming76@ Received 13 May 2010 Accepted 5 July 2010 Academic Editor Claudianoro. Alves Copyright 2010 S. Zhou and C. Mu. 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 devote to investigate the quenching phenomenon for a reaction-diffusion system with coupled singular absorption terms ut ầu - u pp v V vt Av - u-p2v-q2. The solutions of the system quenches in finite time for any initial data are obtained and the blow-up of time derivatives at the quenching point is verified. Moreover under appropriate hypotheses the criteria to identify the simultaneous and nonsimultaneous quenching are found and the four kinds of quenching rates for different nonlinear exponent regions are given. Finally some numerical experiments are performed which illustrate our results. 1. Introduction This paper deals with the following nonlinear parabolic equations with null Neumann boundary conditions ut Au - u P1 v q1 vf Av - u p2v q2 x f e Q X 0 T 0 x f e dQ X 0 T .- 4 11 z u x 0 u0 x v x 0 v0 x x e Q where Pi qi 0 for i 1 2 Q c Rn is a bounded domain with smooth boundary the initial data u0 and v0 are positive smooth and compatible with the boundary data. Because of the singular nonlinearity inner absorption terms of the so-called finite-time quenching may occur for the model. We say that the solution u v of the problem 2 Boundary Value Problems quenches if there exists a time t T TO T denotes the quenching time x .

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