Forward self-similar solution with a moving singularity for a semilinear parabolic equation

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January 2010, 26(1): 313-331. doi: 10.3934/dcds.2010.26.313

Forward self-similar solution with a moving singularity for a semilinear parabolic equation

1.	Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
2.	Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578

Received January 2009 Revised June 2009 Published October 2009

Abstract
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We study the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. It was shown in our previous paper that in some parameter range, the problem has a time-local solution with prescribed moving singularities. Our concern in this paper is the existence of a time-global solution. By using a perturbed Haraux-Weissler equation, it is shown that there exists a forward self-similar solution with a moving singularity. Using this result, we also obtain a sufficient condition for the global existence of solutions with a moving singularity.

Keywords: critical exponent., Semilinear parabolic equation, moving singularity, forward self-similar.

Mathematics Subject Classification: Primary: 35K55; Secondary: 35B3.

Citation: Shota Sato, Eiji Yanagida. Forward self-similar solution with a moving singularity for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 313-331. doi: 10.3934/dcds.2010.26.313

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