# An Analysis of a Mathematical Model Describing Acid-mediated Tumor Invasion

## TL;DR

This paper analyzes a reaction-diffusion mathematical model that explains how acid production by tumors facilitates their invasion into surrounding tissues, supported by theoretical and numerical results.

## Contribution

It offers a rigorous mathematical analysis of a tumor invasion model, including existence, uniqueness, and numerical simulations under different boundary conditions.

## Key findings

- Existence and uniqueness of solutions established.
- Numerical simulations illustrate tumor invasion dynamics.
- Model supports acid-mediated invasion hypothesis.

## Abstract

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 and Dirichlet boundary conditions. We also provide numerical simulations to the solutions considering both boundary conditions.