American Institute of Mathematical Sciences

August  2011, 4(4): 897-906. doi: 10.3934/dcdss.2011.4.897

Singular backward self-similar solutions of a semilinear parabolic equation

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

Received  September 2009 Revised  December 2009 Published  November 2010

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.
Citation: Shota Sato, Eiji Yanagida. Singular backward self-similar solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 897-906. doi: 10.3934/dcdss.2011.4.897
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