Forward self-similar solution with a moving singularity for a semilinear parabolic
Shota Sato - Mathematical Institute, Tohoku University, Sendai 980-8578, Japan (email)
Abstract: 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: Semilinear parabolic equation, forward self-similar, moving singularity, critical exponent.
Received: January 2009; Revised: June 2009; Published: October 2009.
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