Global classical solution of free boundary problem for a coupled system

Abstract

A two-phase free boundary problem for coupled system including three elliptic equations is considered. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The global classical solution of the problem with free boundary Γ:y=g(x,t) between two domains is under search. The global existence and uniqueness of a quasi-stationary problem are proved in multidimensional case.