Abstract
We consider a heterogeneous structure which is stratified in some direction (say x1). The strips are assumed to have very high conductivity which means that the conductivity coefficient a{x1) ranges over |0.+ ∞| oscillating without the usual boundedness assumption (with respect to the L∞-norm) of a and a-1 This problem has been already considered by C.Picard J. Mossino and B.Heron who studied in particular the asymptotic behaviour as ∊-0 of the diffusion equation: boundary condition under the assumption that the sequences (a∊) and (a∊)-1 have limits for the weak topology of L1. In this paper (see also preprint [19]). we propose a new method (convex functionals on measures ranging into L2 which allow us to pass to the limit in (*) when (a∊) and (a∊)1converges ∗-weakly to general Radon measures, say m and tr. Due to the loss of coercivity, the limit of the sequence of solutions (u∊) may have discontinuities whose energy (associated to the singular part of ∊) is concentrated on hyperplanes orthogonal to the On the same way , diffusions surface energies will appear associated with the singular part of m. Extensions to nonlinear problems are also considered.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call