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

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 (C) 2002 John Wiley Sons, Ltd.