Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system

We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of upper $L^{\mathrm{\infty }}$-bounds that exploits the entropic gradient structure of the system.