Limit behaviors of some boundary value problems with high and/or low valued parameters (Q1038571)

This paper deals with the study of a family of bilinear forms depending on two parameters \(\varepsilon\) and \(\sigma\), the first one being understood approaching zero while the second one goes to infinity. The authors give a general framework to characterize the limit problems and to establish strong convergence results. They also deduce a necessary and sufficient condition that guarantees that the two limits commute. Next, this framework is applied to different transmission problems for the elasticity systems (with the Lamé coefficient going to infinity in some subdomains that approach a smooth surface), diffusion problems, and Maxwell systems where one parameter tends to infinity and/or a part of the domain squeezes to a smooth surface. The proofs combine several variational arguments.