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

Giorgia Ciavolella (1, 2) , Benoît Perthame (1, 2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 MAMBA - Modelling and Analysis for Medical and Biological Applications

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 L1 theory developed by M. Pierre and collaborators to these boundary conditions and prove the existence of weak solutions when the initial data has L1 regularity.

Mots clés: Kedem-Katchalsky conditions; membrane boundary conditions; reaction- diffusion equations; mathematical biology

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Giorgia Ciavolella, Benoît Perthame. Existence of a global weak solution for a reaction-diffusion problem with membrane conditions. 2020. ⟨hal-02905180v1⟩