Blow‐up rate estimates for a parabolic system with multiple nonlinearities |
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| Authors: | Xiaowei An Xianfa Song |
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| Institution: | 1. Department of Basic Curriculum, The Chinese People's Armed Police Force Academy, Lang Fang, HeBei 065000, People's Republic of China;2. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, People's Republic of China |
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| Abstract: | In this paper, we study the blow‐up behaviors for the solutions of parabolic systems ut=Δu+δ1e , vt=Δv+µ1u in ? ×(0, T) with nonlinear boundary conditions  Here δi?0, µj?0, pi?0, qj?0 and at least one of δiµjpiqj>0(i, j=1, 2). We prove that the solutions will blow up in finite time for suitable ‘large’ initial values. The exact blow‐up rates are also obtained. Copyright © 2009 John Wiley & Sons, Ltd. |
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| Keywords: | system of parabolic equations nonlinear boundary conditions blow‐up rate blow‐up set maximum principle |
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