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Title: Self-similar solutions of semilinear heat equations with positive speed

Abstract: We classify the smooth self-similar solutions of the semilinear heat equation ut = Delta u + |u|p-1u in Rn & times; (0, T ) satisfying an integral condition for all p > 1 with positive speed. As a corollary, we prove that finite time blowing up solutions of this equation on a bounded convex domain with u(& centerdot;, 0) >= 0 and ut (& centerdot;, 0) >= 0 converges to a positive constant after rescaling at the blow-up point for all p > 1. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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