An analysis of a mathematical model describing acid-mediated tumor invasion

We present a mathematical analysis of a reaction-diffusion model describing acid-mediated tumor invasion. The model describes the spatial distribution and temporal evolution of tumor cells, normal cells, and excess lactic acid concentration. The model assumes that tumor-induced alteration of microenvironmental pH provides a simple but complete mechanism for cancer invasion. We provide results on the existence and uniqueness of a solution considering Neumann boundary condition and comments about the same results with Dirichlet boundary conditions. We also provide numerical simulations to the solutions considering both boundary conditions.