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We consider the semilinear heat equation with a superlinear powernonlinearity in the Sobolev subcritical range. We construct a solution whichblows up in finite time only at the origin, with a completely new blow-upprofile, which is cross-shaped. Our method is general and extends to theconstruction of other solutions blowing up only at the origin, with a largevariety of blow-up profiles, degenerate or not.

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