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On the decay of the solutions of second order parabolic equations with Dirichlet conditions
Author(s) -
Franke Brice
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410518
Subject(s) - isoperimetric inequality , mathematics , bounded function , divergence (linguistics) , dirichlet distribution , order (exchange) , mathematical analysis , parabolic partial differential equation , heat equation , domain (mathematical analysis) , zero (linguistics) , dirichlet problem , function (biology) , boundary value problem , partial differential equation , philosophy , linguistics , finance , evolutionary biology , economics , biology
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)