Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions

Junichi Harada

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arXiv · 1303.5521

Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions

Junichi Harada

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Abstract

This paper is concerned with finite blow-up solutions of the heat equation with nonlinear boundary conditions. It is known that a rate of blow-up solutions is the same as the self-similar rate for a Sobolev subcritical case. A goal of this paper is to construct a blow-up solution whose blow-up rate is different from the self-similar rate for a Sobolev supercritical case.

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Junichi Harada. 2013-03-22. Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions. https://arxiv.org/abs/1303.5521

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