Niveau: Supérieur, Doctorat, Bac+8
Limit behaviors of some boundary value problems with high and/or low valued parameters Salima Hassani?, Serge Nicaise†, Abderrahman Maghnouji‡ 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 and allowing 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. 1 Introduction Some partial differential equations are characterized by the fact that their coefficients are very different in some subpart of the domain where they are set in such a way that their ratio becomes very large. As an example, we can cite the case of the diffusion problem [15]: ?div (a?u) = f in D, where a = 1 in a fixed part of the domain D and a goes to infinity in the remainder Da of the domain D. In that case, it is not difficult to obtain the limit problem, see for instance [15]. In a similar manner, it is not difficult to obtain the limit problem of the above problem if a remains fixed but the sub-domain squeezes to a smooth hypersurface of codimension 1.
- find u? ?
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- unique solution
- limit procedures
- respective spaces
- ?université de valenciennes et du hainaut cambrésis