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.