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On the decay of the solutions of second order parabolic equations with Dirichlet conditions

✍ Scribed by Brice Franke

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
209 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

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. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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On Time Periodic Solutions of the Dirich
On Time Periodic Solutions of the Dirichlet Problem for Degenerate Parabolic Equations of Nondivergence Type
✍ Yoshikazu Giga; Noriko Mizoguchi πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 206 KB

In this paper, we are concerned with the existence of periodic solutions of a quasilinear parabolic equation t with the Dirichlet boundary condition, where ⍀ is a smoothly bounded domain in N R and f is a given function periodic in time defined on ⍀ = R. Our results depend on the first eigenvalue o