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

  • Frank Merle

    IHÉS, Bures-sur-Yvette, France; CY Cergy Paris Université, Cergy-Pontoise, France
  • Hatem Zaag

    Université Sorbonne Paris Nord, Villetaneuse, France
On degenerate blow-up profiles for the subcritical semilinear heat equation cover

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Abstract

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.

Cite this article

Frank Merle, Hatem Zaag, On degenerate blow-up profiles for the subcritical semilinear heat equation. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1493