An example of blowup for a degenerate parabolic equation with a nonlinear boundary condition

Chipot, M; Filo, J (1998). An example of blowup for a degenerate parabolic equation with a nonlinear boundary condition. Zeitschrift für Analysis und ihre Anwendungen, 17(1):89-102.

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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 $u_x\geq\eta>0,\ 1<p<2$ , with nonlinear boundary condition $a(u_x(1,t))=|u|^{q-2}u(1,t)$ , is considered. It is proved that if $qp-3p+2>0$ , then the solutions blow up in finite time. Moreover, estimates on the blow-up profile (in $x$ ) and the blow-up rate (in $t$ ) for $x=1$ are derived.

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	regularity results; nonlocal variational inequalities
Language:	English
Date:	1998
Deposited On:	26 Jul 2010 13:35
Last Modified:	23 Nov 2012 14:43
Publisher:	European Mathematical Society
ISSN:	0232-2064
Publisher DOI:	10.4171/ZAA
Official URL:	http://www.math.ethz.ch/EMIS/journals/ZAA/
Related URLs:	http://www.zentralblatt-math.org/zbmath/search/

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