Membrane problems: existence of solutions and numerical analysis


Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions, describing the flow through the membrane, are compatible with mass conservation and energy dissipation, and are called the Kedem-Katchalsky conditions. A huge literature deeply analyses usual reaction-diffusion systems and we extended to membrane problems an existence theory compatible with the L^1 bounds. In particular, we are interested in developing a theory of weak solutions when the initial data has only L^1 regularity and the reaction terms are, for instance, quadratic. A classical numerical study on reaction-diffusion systems concerns Turing instability. We illustrate patterns formation and their discontinuous behaviour passing through the membrane.

Jan 18, 2021 2:00 PM
Giorgia Ciavolella
Giorgia Ciavolella
PhD student in Applied Mathematics