Analysis of bulk-surface reaction-sorption-diffusion systems with Langmuir-type adsorption

Abstract

We consider a class of bulk-surface reaction-adsorption-diffusion systems, i.e. a coupled system of reaction-diffusion systems on a bounded domain $\Omega \subseteq R^d$ (bulk phase) and its boundary $\Sigma =\partial \Omega$ (surface phase), which are coupled via nonlinear normal flux boundary conditions. In particular, this class includes a heterogeneous catalysis model with Fickian bulk and surface diffusion and nonlinear adsorption of Langmuir type, i.e. transport from the bulk phase to the active surface, and desorption. For this model, we obtain well-posedness, positivity and global-in-time existence of solutions under some realistic structural conditions on the chemical reaction network and the sorption model. We work in appropriate Sobolev-Slobodetskii settings, where we aim for a wide range for the integrability index, including in particular values $p<d$.