Existence of Solution of a Free Boundary Problem for Reaction–Diffusion Systems

In this paper, we prove the existence of a solution of a novel free boundary problem for reaction-diffusion systems describing growth of biological tissues due to cell influx and proliferation. For this aim, we transform it into a problem with fixed boundary, through a change of variables. The new problem thus obtained has space and time dependent coefficients with nonlinear terms. We then prove the existence of a solution for the corresponding linear problem, and deduce the existence of a solution for the nonlinear problem using the fixed point theorem. Finally, we return to the problem with free boundary to conclude the existence of its solution.