Well-posedness and fast-diffusion limit for a bulk–surface reaction–diffusion system

Abstract

We analyze a certain class of coupled bulk–surface reaction–drift–diffusion systems arising in the modeling of signalling networks in biological cells. The coupling is by a nonlinear Robin-type boundary condition for the bulk variable and a corresponding source term on the cell boundary. For reaction terms with at most linear growth and under different regularity assumptions on the data we prove the existence of weak and classical solutions. In particular, we show that solutions grow at most exponentially with time. Furthermore, we rigorously derive an asymptotic reduction to a non-local reaction–drift–diffusion system on the membrane in the fast-diffusion limit.