Singular backward self-similar solutions of a semilinear parabolic equation

Shota Sato; Eiji Yanagida

doi:10.3934/dcdss.2011.4.897

Article Contents

2011, Volume 4, Issue 4: 897-906. Doi: 10.3934/dcdss.2011.4.897

This issue Previous Article A Liouville-type theorem for some Weingarten hypersurfaces Next Article An eigenvalue problem related to blowing-up solutions for a semilinear elliptic equation with the critical Sobolev exponent

Singular backward self-similar solutions of 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: September 2009

Revised: December 2009

Published: August 2011

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Abstract

We consider a parabolic partial differential equation with power nonlinearity. Our concern is the existence of a singular solution whose singularity becomes anomalous in finite time. First we study the structure of singular radial solutions for an equation derived by backward self-similar variables. Using this, we obtain a singular backward self-similar solution whose singularity becomes stronger or weaker than that of a singular steady state.

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

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References

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