# An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition

### Michel Chipot

Universität Zürich, Switzerland### Ján Filo

Comenius University, Bratislava, Slovak Republic

## Abstract

In this paper, a nonlinear parabolic equation of the form $u_t = (a(u_x))_x$ for $x \in (0, 1), t > 0, a(u_x) = |u_x|^{p–2}u_x$ if $u_x ≥ \eta > 0, 1 < p < 2$, with nonlinear boundary condition $a(u_x r(1, t)) = |u|^{q–2} u(l,t)$ is considered. It is proved that if $qp - 3p + 2 > 0$, then the solutions blow up in finite time. Moreover, estimates on the blowup profile (in $x$) and the blowup rate (in $t$) for $x = 1$ are derived.

## Cite this article

Michel Chipot, Ján Filo, An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition. Z. Anal. Anwend. 17 (1998), no. 1, pp. 89–102

DOI 10.4171/ZAA/810