On a Semi-Coercive Quasi-Variational Inequality

摘要

One feature of the so-called quasi-variational problems is that the constraints are not given in advance. The problem considered in this paper is related to the description of a stationary temperature distribution inside a material with thermally semi-permeable boundary (here are the constraints) in the case where the exterior temperature varies proportionally to some average of the heat flux crossing the boundary (here is the dependence of the constraints on the solution). Some existence results were obtained in a previous work by the authors, assuming that the heat balance equation is coercive, a condition which eventually yields solutions for any forcing term. Here we deal with a weakened form of this condition, the semi-coercive case, which, in some respects, is physically more natural. A sufficient and almost necessary condition on the forcing term is obtained for the existence of solutions.