Blow‐up analysis for a system of heat equations coupled via nonlinear boundary conditions |
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| Authors: | Xianfa Song |
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| Affiliation: | Department of Mathematics, China University of Mining and Technology (Beijing), Peking 100083, People's Republic of ChinaDepartment of Mathematics, China University of Mining and Technology (Beijing), Peking 100083, People's Republic of China=== |
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| Abstract: | In this paper, we study a system of heat equations  coupled via nonlinear boundary conditions  (1) Here p, q>0. We prove that the solutions always blow up in finite time for non‐trivial and non‐negative initial values. We also prove that the blow‐up occurs only on SR = ?BR for Ω = BR = {x ? ?n:|x|<R}and  under some assumptions on the initial values. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | system of heat equations nonlinear boundary conditions blow‐up rate blow‐up set |
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