Limit behaviors of some boundary value problems with high and/or low valued parameters

Abstract

The first aim of this paper is to give a general variational framework for bilinear forms depending on two parameters tending to zero and to infinity respectively, allowing us to analyze the three limit problems. Secondly, we give different illustrative applications for transmission problems involving some elasticity systems, diffusion problems, and Maxwell systems where one parameter tends to infinity and/or a part of the domain squeezes to a smooth surface. These limit procedures lead to new transmission problems, like a coupling between the Lamé system and the Stokes system.