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1995 Unstable blow-up patterns
Debora Amadori
Differential Integral Equations 8(8): 1977-1996 (1995).

Abstract

Consider the semilinear heat equation $u_{t}=\Delta u + u^{p}$, $t>0$, in an open set $\Omega \subset \mathbf {R}^N$, $p>1$. For every $a \in \Omega$, we construct solutions which blow up at $a$, at a finite time $T$, according to a variety of specific asymptotic behaviors. These blow-up patterns are unstable. The corresponding solutions have an arbitrary large number of local maxima, collapsing at $a$ for $t=T$.

Citation

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Debora Amadori. "Unstable blow-up patterns." Differential Integral Equations 8 (8) 1977 - 1996, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0839.35062
MathSciNet: MR1348961

Subjects:
Primary: 35K60
Secondary: 35B40

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.8 • No. 8 • 1995
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