On a Relaxed Cahn–Hilliard Tumor Growth Model with Single-Well Potential and Degenerate Mobility

Abstract.

We consider a phase-field system modeling solid tumor growth. This system consists of a Cahn–Hilliard equation coupled with a nutrient equation. The former is characterized by a degenerate mobility and a singular potential. Both equations are subject to suitable reaction terms which model proliferation and nutrient consumption. Chemotactic effects are also taken into account. Adding an elliptic regularization, depending on a relaxation parameter [Formula: see text], in the equation for the chemical potential, we prove the existence of a weak solution to an initial and boundary value problem for the relaxed system. Then, we let [Formula: see text] go to zero, and we recover the existence of a weak solution to the original system.