Appearance of anomalous singularities  in a semilinear parabolic equation

Shota Sato; Eiji Yanagida

doi:10.3934/cpaa.2012.11.387

Article Contents

2012, Volume 11, Issue 1: 387-405. Doi: 10.3934/cpaa.2012.11.387

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Appearance of anomalous singularities in a semilinear parabolic equation

Shota Sato^1, and
Eiji Yanagida^2,

1.
Mathematical Institute, Tohoku University, Sendai 980-8578
2.
Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551

Received: February 28, 2010

Revised: October 31, 2010

Published: December 2011

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Abstract

The Cauchy problem for a parabolic partial differential equation with a power nonlinearity is studied. It is known that in some parameter range, there exists a time-local solution whose singularity has the same asymptotics as that of a singular steady state. In this paper, a sufficient condition for initial data is given for the existence of a solution with a moving singularity that becomes anomalous in finite time.

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Mathematics Subject Classification: Primary: 35K55; Secondary: 35B33.

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