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: v Research Article Blowup Analysis for a Semilinear Parabolic System with Nonlocal Boundary Condition | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 516390 14 pages doi 2009 516390 Research Article Blowup Analysis for a Semilinear Parabolic System with Nonlocal Boundary Condition Yulan Wang1 and Zhaoyin Xiang2 1 School of Mathematics and Computer Engineering Xihua University Chengdu 610039 China 2 School of Applied Mathematics University of Electronic Science and Technology of China Chengdu 610054 China Correspondence should be addressed to Zhaoyin Xiang zxiangmath@ Received 23 July 2009 Accepted 26 October 2009 Recommended by Gary Lieberman This paper deals with the properties of positive solutions to a semilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence which shows the important influence of nonlocal boundary. And then we establish the precise blowup rate estimate for small weighted nonlocal boundary. Copyright 2009 Y. Wang and Z. Xiang. 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 In this paper we devote our attention to the singularity analysis of the following semilinear parabolic system ut - àu vp vt - àv uq x e Q t 0 with nonlocal boundary condition u x t J f x y u y t dy v x t J g x y v y t dy x e dQ t 0 and initial data u x 0 u0 x v x 0 vo x x e Q 2 Boundary Value Problems where Q c RN is a bounded connected domain with smooth boundary dQ p and q are positive parameters. Most physical settings lead to the default assumption that the functions f x y g x y defined for x e dQ y e Q are nonnegative and continuous and that the initial data u0 x v0 x e C1 Q are nonnegative which are mathematically convenient and currently followed throughout this paper. We also assume that u0 v0 satisfies the compatibility condition on ÔQ and that f x 0 and g x .
