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Explicit decay bounds in some quasilinear one‐dimensional parabolic problems
Author(s) -
Philippin G. A.,
VernierPiro S.
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990125)22:2<101::aid-mma23>3.0.co;2-f
Subject(s) - mathematics , parabolic partial differential equation , heat equation , order (exchange) , diffusion , mathematical analysis , maximum principle , process (computing) , partial differential equation , mathematical optimization , optimal control , physics , thermodynamics , computer science , finance , economics , operating system
In the first part of this paper we study a thermal diffusion process described by a semilinear parabolic problem and we introduce a new maximum principle in order to obtain explicit decay bounds for the temperature and its gradient. In the second part we find analogous bounds for the so‐called ground water equation in a more general form. Copyright © 1999 John Wiley & Sons, Ltd.