Blow-up at space infinity of a  solution with a  moving singularity for a semilinear parabolicequation

Shota Sato

doi:10.3934/cpaa.2011.10.1225

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2011, Volume 10, Issue 4: 1225-1237. Doi: 10.3934/cpaa.2011.10.1225

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Blow-up at space infinity of a solution with a moving singularity for a semilinear parabolic equation

Shota Sato^1,

1.
Mathematical Institute, Tohoku University, Sendai 980-8578

Received: July 2010

Revised: October 2010

Published: July 2011

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Abstract

We consider 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 solution with a moving singularity that becomes anomalous in finite time. Our concern is a blow-up solution with a moving singularity. In this paper, we show that there exists a solution with a moving singularity such that it blows up at space infinity.

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Mathematics Subject Classification: Primary: 35K58; Secondary: 35B33, 35B44.

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References

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