Differential and Integral Equations

Unstable blow-up patterns

Debora Amadori

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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 $t=T$.

Article information

Source
Differential Integral Equations, Volume 8, Number 8 (1995), 1977-1996.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056136

Mathematical Reviews number (MathSciNet)
MR1348961

Zentralblatt MATH identifier
0839.35062

Subjects
Primary: 35K60: Nonlinear initial value problems for linear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Amadori, Debora. Unstable blow-up patterns. Differential Integral Equations 8 (1995), no. 8, 1977--1996. https://projecteuclid.org/euclid.die/1369056136


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