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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 89–102
DOI: 10.4171/ZAA/810

Published online: 1998-03-31

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

Michel Chipot[1] and Ján Filo[2]

(1) Universität Zürich, Switzerland
(2) Comenius University, Bratislava, Slovak Republic

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.

Keywords: Degenerate parabolic equations, nonlinear boundary conditions, blowup

Chipot Michel, Filo Ján: An Example of Blowup for a Degenerate Parabolic Equation with a Nonlinear Boundary Condition. Z. Anal. Anwend. 17 (1998), 89-102. doi: 10.4171/ZAA/810