SHADOW LIMIT FOR PARABOLIC-ODE SYSTEMS THROUGH A CUT-OFF ARGUMENT

International audienceWe study a shadow limit (the infinite diffusion coefficient-limit) of a system of ODEs coupled with a diagonal system of semilinear heat equations in a bounded domain with homogeneous Neumann boundary conditions. The recent convergence proof by the energy approach from [19], developed for the case of a single PDE, is revisited and generalized to the case of the coupled system. Furthermore, we give a new convergence proof relying on the introduction of a well-prepared related cutoff system and on a construction of the barrier functions and comparison test functions , new in the literature. It leads to the L ∞-estimates proportional to the inverse of the diffusion coefficient