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: BLOWUP FOR DEGENERATE AND SINGULAR PARABOLIC SYSTEM WITH NONLOCAL SOURCE | BLOWUP FOR DEGENERATE AND SINGULAR PARABOLIC SYSTEM WITH NONLOCAL SOURCE JUN ZHOU CHUNLAI MU AND ZHONGPING LI Received 23 January 2006 Revised 3 April 2006 Accepted 7 April 2006 We deal with the blowup properties of the solution to the degenerate and singular parabolic system with nonlocal source and homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained. Furthermore under certain conditions it is proved that the blowup set of the solution is the whole domain. Copyright 2006 Jun Zhou et al. 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 following degenerate and singular nonlinear reactiondiffusion equations with nonlocal source xq1 ut - xr1 ux x vp1 dx x t G 0 a X 0 T 0 xq2Vt - xr2Vx x J up2dx x t G 0 a X 0 T 11 u 0 t u a t v 0 t v a t 0 t G 0 T u x 0 u0 x v x 0 v0 x x G 0 a where u0 x v0 x G C2 a D for some a G 0 1 are nonnegative nontrivial functions. u0 0 u0 a v0 0 v0 a 0 u0 x 0 v0 x 0 u0 v0 satisfy the compatibility condition T 0 a 0 r1 r2 G 0 1 q11 r1 0 q21 r2 0 and p1 1 p2 1. Let D 0 a and ot D X 0 t D and ot are their closures respectively. Since q1 r1 0 q2 r2 0 the coefficients of ut ux uxx and vt vx vxx may tend to 0 or TO as x tends to 0 we can regard the equations as degenerate and singular. Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID 21830 Pages 1-19 DOI BVP 2006 21830 2 Blowup for degenerate and singular parabolic system Floater 9 and Chan and Liu 4 investigated the blowup properties of the following degenerate parabolic problem xqut - Uxx up x t e 0 a X 0 T u 0 t u a t 0 t e 0 T u x 0 u0 x x e 0 a where q 0 and p 1. Under certain .
