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Blow-up estimates for system of heat equations coupled via nonlinear boundary flux

✍ Scribed by Lizhong Zhao; Sining Zheng

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
124 KB
Volume
54
Category
Article
ISSN
0362-546X

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Blow-up analysis for a system of heat eq
Blow-up analysis for a system of heat equations coupled via nonlinear boundary conditions
✍ Xianfa Song πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 128 KB πŸ‘ 1 views

## 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 value

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The paper deals with the blow-up rate of positive solutions to the system l 11 l 12 l 21 l 22 Ε½ . u s u q u Β¨, Β¨s Β¨q u Β¨with boundary conditions u 1, t s t x x t x x x Ε½ p 11 p 12 .Ε½ . Ε½ . Ε½ p 21 p 22 .Ε½ . u Β¨1, t and Β¨1, t s u Β¨1, t . Under some assumptions on the x Ε½ . Ε½ . Ε½ . matrices L s l and

Blow-up analysis for a system of heat eq
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✍ Xianfa Song πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 273 KB

We consider a system of heat equations u t = βˆ†u and v t = βˆ†v in Ω Γ— (0, T ) completely coupled by nonlinear boundary conditions βˆ‚u βˆ‚Ξ· = e pv u Ξ± , βˆ‚v βˆ‚Ξ· = u q e Ξ²v on βˆ‚β„¦ Γ— (0, T ). We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow