Mathematics

 We study a diffuse-phase model for tumor growth, which is a fourth-order PDEs system involving a Cahn-Hilliard equation. This model approximates, through a parameter \epsilon, a sharp interface model for tumor growth. We prove that the solutions of the PDEs system converge to the solution of a free-boundary problem as \epsilon goes to zero, using a standard technique due to Sandier and Serfaty and known as Gamma convergence for gradient flows. We finally discuss some open problems related to our derivation.