Nonexistence of backward self-similar blowup solutions to a supercritical semilinear heat equation |
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Authors: | Noriko Mizoguchi |
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Institution: | aDepartment of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan |
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Abstract: | We consider a Cauchy problem for a semilinear heat equation with p>pS where pS is the Sobolev exponent. If u(x,t)=(T−t)−1/(p−1)φ((T−t)−1/2x) for xRN and t0,T), where φ is a regular positive solution of then u is called a backward self-similar blowup solution. It is immediate that (P) has a trivial positive solution κ≡(p−1)−1/(p−1) for all p>1. Let pL be the Lepin exponent. Lepin obtained a radial regular positive solution of (P) except κ for pS<p<pL. We show that there exist no radial regular positive solutions of (P) which are spatially inhomogeneous for p>pL. |
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Keywords: | Blowup Backward self-similar Supercritical elliptic equation Critical exponent |
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