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December 1996 Critical Blow-Up for Quasilinear Parabolic Equations in Exterior Domains
Ryuichi SUZUKI
Tokyo J. Math. 19(2): 397-409 (December 1996). DOI: 10.3836/tjm/1270042528

Abstract

We consider nonnegative solutions to the exterior Dirichlet problem for quasilinear parabolic equations $u_t=\Delta u^m+u^p$ with $p=m+2/N$ and $m\geq 1$. In this paper we show that when $N\geq 3$ all nontrivial solutions to above problem blow up in finite time. For this aim, it is important to study the asymptotic behavior of solutions to the exterior Dirichlet problem for the quasilinear parabolic equations $u_t=\Delta u^m$.

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Ryuichi SUZUKI. "Critical Blow-Up for Quasilinear Parabolic Equations in Exterior Domains." Tokyo J. Math. 19 (2) 397 - 409, December 1996. https://doi.org/10.3836/tjm/1270042528

Information

Published: December 1996
First available in Project Euclid: 31 March 2010

zbMATH: 0868.35064
MathSciNet: MR1425157
Digital Object Identifier: 10.3836/tjm/1270042528

Rights: Copyright © 1996 Publication Committee for the Tokyo Journal of Mathematics

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Vol.19 • No. 2 • December 1996
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