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 Simultaneous versus Nonsimultaneous Blowup for a System of Heat Equations Coupled Boundary Flux | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 75258 7 pages doi 2007 75258 Research Article Simultaneous versus Nonsimultaneous Blowup for a System of Heat Equations Coupled Boundary Flux Mingshu Fan and Lili Du Received 5 November 2006 Revised 18 January 2007 Accepted 23 March 2007 Recommended by Gary M. Lieberman This paper deals with a semilinear parabolic system in a bounded interval completely coupled at the boundary with exponential type. We characterize completely the range of parameters for which nonsimultaneous and simultaneous blowup occur. Copyright 2007 M. Fan and L. Du. 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 consider the positive blowup solution to the following parabolic problem Ut Uxx Vt vxx x t e 0 L X 0 T -ux 0 t ep11u 0 t p12v 0 t -Vx 0 t ep21U 0 f p22v 0 f t e 0 T Ux L t 0 Vx L t 0 t e 0 T U x 0 U0 x v x 0 V0 x x e 0 L where we assume the parameters pij 0 i j 1 2 p11 p22 0 and p21 p12 0 which ensure that completely coupled with the nontrivial nonlinear boundary flux. The initial values U0 x V0 x are positive nontrivial bounded and compatible with the boundary data and smooth enough to guarantee that U V are regular. The study of reaction-diffusion systems has received a great deal of interest in recent years and has been used to model for example heat transfer population dynamics and chemical reactions see 1 and references therein . The parabolic system like can be used to describe for example heat propagations in mixed solid nonlinear media with nonlinear boundary flux. The nonlinear Nuemann boundary values in coupling 2 Boundary Value Problems the two heat equations represent some cross-boundary flux. Let T denote the maximal existence time for the solution u v . If it is infinite we say
