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On degenerate blow-up profiles for the subcritical semilinear heat equation (2205.06795v1)
Published 13 May 2022 in math.AP
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.