## Differential and Integral Equations

### 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