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arXiv:2205.06795 [math.AP]AbstractReferencesReviewsResources

On degenerate blow-up profiles for the subcritical semilinear heat equation

Frank Merle, Hatem Zaag

Published 2022-05-13Version 1

We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the origin, with a completely new blow-up profile, which is cross-shaped. Our method is general and extends to the construction of other solutions blowing up only at the origin, with a large variety of blow-up profiles, degenerate or not.

Comments: 61 pages
Categories: math.AP
Subjects: 35L05, 35K10, 35K58, 35B44, 35B40
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