Shadow limit for parabolic-ODE systems through a cut-off argument - Marciniak-Czochra, Anna; Mikelić, Andro (Rad Hrvatske Akademije Znanosti i Umjetnosti, Razred za Matematičke, Fizičke, Kemijske i Tehničke Znanosti, 2017)
We study a shadow limit (the infinite diffusion coefficientlimit) 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 cut-off 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.