In this project we will analyze in a mathematically rigorous way a free boundary value problem consisting of a elliptic-hyperbolic system of partial differential equations related to the Hele-Shaw problem. The problem in the project models the growth of a tumor and takes in consideration the following possibilities for the state of a tumor cell: proliferating cells, quiescent cells or necrotic cells; the model also take in consideration the nutrient concentration in the tumor. The equations hold in a time varying domain depending on the other variables of the problem. The main objective of the project is a local in time existence of solutions for the system, as well as their uniqueness.
News published in Agência FAPESP Newsletter about the scholarship: