Interior derivative blow-up for quasilinear parabolic equations

Yoshikazu Giga

doi:10.3934/dcds.1995.1.449

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1995, Volume 1, Issue 3: 449-461. Doi: 10.3934/dcds.1995.1.449

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Interior derivative blow-up for quasilinear parabolic equations

Yoshikazu Giga^1,

1.
Department of Mathematics, Hokkaido University, Sapporo 060

Received: April 30, 1995

Published: June 1995

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Abstract

We give examples of a bounded solution whose gradient blows up in a finite time but it stays bounded on the boundary for a class of quasilinear parabolic equations with zero boundary data. The method reflects a geometric argument for curve evolution equations.

Keywords:

quasilinear parabolic equations,
blow-up.

Mathematics Subject Classification: 35K55.

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