Existence of a global weak solution for a reaction-diffusion problem with membrane conditions

Giorgia Ciavolella, Benoît Perthame

Published 2020-07-23Version 1

Several problems, issued from physics or biology, lead to parabolic equations set in two sub-domains separated by a membrane. The corresponding boundary conditions are compatible with mass conservation and are called the Kedem-Katchalsky conditions. In these models, written as reaction-diffusion systems, the reaction terms have a quadratic behaviour. We adapt the $L^1$ theory developed by M. Pierre and collaborators to these boundary conditions and prove the existence of weak solutions when the initial data has $L^1$ regularity.