Existence of solution of a free boundary problem for reaction-diffusion systems

In this paper, we prove the existence of 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 solution for the corresponding linear problem, and deduce the existence of 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.