## Differential and Integral Equations

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

### Unstable blow-up patterns

#### 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