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The blow-up property for a system of heat equations with nonlinear boundary conditions

Authors:	Lin Zhigui Xie Chunhong Wang Mingxin

Institution:	(1) Department of Mathematics, Nanjing University, 210093 Nanjing;(2) Department of Mathematics and Mechanics, Southeast University, 210018 Nanjing

Abstract:	This paper deals with the blow-up properties of solutions to the systems u _t=Δu,v_t=Δv in B _RX(0,T) subject to nonlinear boundary conditions $\frac{{\partial u}}{{\partial \eta }} = \upsilon ^p ,\frac{{\partial \upsilon }}{{\partial \eta }} = u^q$ , in S _RX(0,T). It is shown that under certain conditions the solution blows up at a finite time and the blow-up only occurs on the boundary. The self-similar solution for the one-dimensional case has been studied. Moreover, the exact blow-up rates are also derived. The third author's work was supported by the National Natural Science Foundation of China.

Keywords:	35K55 35K60 35B35
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