## Tokyo Journal of Mathematics

### Critical Blow-Up for Quasilinear Parabolic Equations in Exterior Domains

Ryuichi SUZUKI

#### 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 $u_t=\Delta u^m$.

#### Article information

Source
Tokyo J. Math., Volume 19, Number 2 (1996), 397-409.

Dates
First available in Project Euclid: 31 March 2010

https://projecteuclid.org/euclid.tjm/1270042528

Digital Object Identifier
doi:10.3836/tjm/1270042528

Mathematical Reviews number (MathSciNet)
MR1425157

Zentralblatt MATH identifier
0868.35064

#### Citation

SUZUKI, Ryuichi. Critical Blow-Up for Quasilinear Parabolic Equations in Exterior Domains. Tokyo J. Math. 19 (1996), no. 2, 397--409. doi:10.3836/tjm/1270042528. https://projecteuclid.org/euclid.tjm/1270042528