Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition
✍ Scribed by Julián López Gómez; Viviana Márquez; Noemí Wolanski
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 784 KB
- Volume
- 92
- Category
- Article
- ISSN
- 0022-0396
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## 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
The paper deals with the blow-up rate of positive solutions to the system l 11 l 12 l 21 l 22 Ž . u s u q u ¨, ¨s ¨q u ¨with boundary conditions u 1, t s t x x t x x x Ž p 11 p 12 .Ž . Ž . Ž p 21 p 22 .Ž . u ¨1, t and ¨1, t s u ¨1, t . Under some assumptions on the x Ž . Ž . Ž . matrices L s l and