Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds

We address homogenization problems of variational inequalities for the p-Laplace operator in a domain of Rn (n ? 3, p ? [2, n)) periodically perforated by balls of radius O(??) where ? > 1 and ? is the size of the period. The perforations are distributed along a (n ? 1)-dimensional manifold ? , and we impose constraints for solutions and their fluxes (associated with the p-Laplacian) on the boundary of the perforations. These constraints imply that the solution is positive and that the flux is bounded from above by a negative, nonlinear monotonic function of the solution multiplied by a parameter ? ?? , ? ? R and ? is a small parameter that we shall make to go to zero. We analyze different relations between the parameters p, n, ?, ? and ?, and obtain homogenized problems which are completely new in the literature even for the case p = 2.This work has been partially supported by the Spanish grant MINECO:MTM2013-44883-P

Residual distribution schemes on quadrilateral meshes

We propose an investigation of the residual distribution schemes for the numerical approximation of two dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the Upwinding concept is given, and a Lax-Wendroff like theorem is adapted for consistency. We show how to retrieve many variants of standard first and second order accurate schemes. They are proven to satisfy this theorem. An important part of this paper is devoted to the validation of these schemes by various numerical tests for scalar equations and Euler equations system for compressible fluid dynamics on non Cartesian grids.In particular, second order accuracy is reached by an adaptation of the Linear preserving property to quadrangle meshes. We discuss several choices as well as the convergence of iterative method to steady state. We also provide examples of schemes that are not constructed from an upwinding principle.

Promontofixation : quelles prothèses choisir ? Étude expérimentale et clinique

International audienc

Modeling the circulation of a disease between two host populations on non coincident spatial domains

We derive a reaction–diffusion system modeling the spatial propagation of a disease with kinetics occurring on distinct spatial domains. This corresponds to the actual invasion of a disease from a species living in a given spatial domain toward a second species living in a different spatial domain. We study the global existence of solutions and discuss the long time behavior of solutions. Then we consider a special case, based on a model of brain worm infection from white-tailed deer to moose populations, for which we discuss the invasion success/failure process and disprove a conjecture stated in an earlier work