A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation |
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Authors: | Peter Poláčik Pavol Quittner |
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Institution: | 1. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;2. Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia |
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Abstract: | We consider the semilinear parabolic equation ut=Δu+up on RN, where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions defined for all x∈RN and t∈R. Our main result asserts that there are no positive radially symmetric bounded entire solutions. Then we consider radial solutions of the Cauchy problem. We show that if such a solution is global, that is, defined for all t?0, then it necessarily converges to 0, as t→∞, uniformly with respect to x∈RN. |
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Keywords: | 35k15 35b40 |
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