On the decay of the solutions of second order parabolic equations with Dirichlet conditions |
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| Authors: | Brice Franke |
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| Institution: | Ruhr‐Universit?t Bochum, Fakult?t für Mathematik, Universit?tsstr. 150, 44780 Bochum, GermanyPhone: +49 234 3228588, Fax: +49 234 3214039 |
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| Abstract: | We use rearrangement techniques to investigate the decay of the parabolic Dirichlet problem in a bounded domain. The coefficients of the second order term are used to introduce an isoperimetric problem. The resulting isoperimetric function together with the divergence of the first order coefficients and the value distribution of the zero order part are then used to construct a symmetric comparison equation having a slower heat‐flow than the original equation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Isoperimetric problem heat‐flow rearrangement Dirichlet problem divergence semigroup |
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