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Blow-up analysis for a system of heat equations coupled via nonlinear boundary conditions

✍ Scribed by Xianfa Song

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
128 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper, we study a system of heat equations $u_t=\Delta u, , v_t=\Delta v,{\rm in},\Omega\times(0,T)$ coupled via nonlinear boundary conditions
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 S~R~ = βˆ‚B~R~ for Ξ© = B~R~ = {x Ο΅ ℝ^n^:|x|<R}and $C_1(T-t)^{-1/2q}\le u(R, t) \le C_2(T-t)^{-1/2q},,\log(c_3(T-t)^{-(q+1)/2pq})\le v(R, t)\le \log(C_4(T-t)^{-(q+1)/2pq})$ under some assumptions on the initial values. Copyright Β© 2007 John Wiley & Sons, Ltd.

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