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The asymptotic self-similar behavior for the quasilinear heat equation with nonlinear boundary condition

✍ Scribed by Zhiwen Duan

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
877 KB
Volume
58
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function v(y, t) = (Tt) 1/(2p+Ξ±-2) u((Tt) (p-1)/(2p+Ξ±-2) y, t), behaves as t β†’ T like a nontrivial self-similar profile.

πŸ“œ SIMILAR VOLUMES

On Critical Exponents for the Heat Equat
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In this paper we consider the heat equation u s ⌬ u in an unbounded domain t N Ε½ . ⍀;R with a partly Dirichlet condition u x, t s 0 and a partly Neumann condition u s u p on the boundary, where p ) 1 and is the exterior unit normal on the boundary. It is shown that for a sectorial domain in R 2 and