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

Frank Merle; Hatem Zaag

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

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arxiv 2205.06795 v1 pith:NWCQN35Q submitted 2022-05-13 math.AP

Frank Merle , Hatem Zaag This is my paper · ORCID

classification math.AP

keywords blow-updegenerateequationheatonlyoriginprofilessemilinear

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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.

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