A Coupled Ligand-Receptor Bulk-Surface System on a Moving Domain: Well Posedness, Regularity, and Convergence to Equilibrium

TERRA, JOANA; ELLIOTT, CHARLES M.; ALPHONSE, AMAL

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

SIAM PUBLICATIONS

Año: 2018 vol. 50 p. 1544 - 1592

0036-1410

We prove existence, uniqueness, and regularity for a reaction-diffusion system ofcoupled bulk-surface equations on a moving domain modeling receptor-ligand dynamics in cells. Thenonlinear coupling between the three unknowns is through the Robin boundary condition for thebulk quantity and the right-hand sides of the two surface equations. Our results are new even inthe nonmoving setting, and in this case we also show exponential convergence to a steady state. Theprimary complications in the analysis are indeed the nonlinear coupling and the Robin boundarycondition. For the well posedness and essential boundedness of solutions we use several De Giorgi-type arguments, and we also develop some useful estimates to allow us to apply a Steklov averagingtechnique for time-dependent operators to prove that solutions are strong. Some of these auxiliaryresults presented in this paper are of independent interest by themselves.