Rates of convergence to zero for a semilinear parabolic equation with a critical exponent |
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Authors: | Christian Stinner |
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Affiliation: | Fakultät für Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany |
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Abstract: | We study nonnegative solutions to the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the sense of Joseph and Lundgren. We establish the rate of convergence to zero of solutions that start from initial data which are near the singular steady state. In the critical case, this rate contains a logarithmic term which does not appear in the supercritical case and makes the calculations more delicate. |
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Keywords: | 35B33 35B40 35K57 |
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