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Note on a versatile Liapunov functional: applicability to an elliptic equation

✍ Scribed by J. N. Flavin; S. Rionero

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 69 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.338

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✦ Synopsis

Abstract

A novel, very effective Liapunov functional was used in previous papers to derive decay and asymptotic stability estimates (with respect to time) in a variety of thermal and thermo‐mechanical contexts. The purpose of this note is to show that the versatility of this functional extends to certain non‐linear elliptic boundary value problems in a right cylinder, the axial co‐ordinate in this context replacing the time variable in the previous one. A steady‐state temperature problem is considered with Dirichlet boundary conditions, the condition on the boundary being independent of the axial co‐ordinate. The functional is used to obtain an estimate of the error committed in approximating the temperature field by the two‐dimensional field induced by the boundary condition on the lateral surface. Copyright © 2002 John Wiley & Sons, Ltd.

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