Continuation beyond interior gradient blow-up in a semilinear parabolic equation

Marek Fila; Johannes Lankeit

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arXiv · 1902.01127

Continuation beyond interior gradient blow-up in a semilinear parabolic equation

Marek Fila·Johannes Lankeit

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Abstract

It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of such solutions after gradient blow-up. This continuation is global in time and we give an example when it never becomes a classical solution again.

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Marek Fila, Johannes Lankeit. 2019-02-04. Continuation beyond interior gradient blow-up in a semilinear parabolic equation. https://arxiv.org/abs/1902.01127

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