| Abstract: |
| We consider a phase-field system modelling solid tumour growth. This system consists of a Cahn-Hilliard equation coupled with a nutrient equation. The former is characterised by a degenerate mobility and a singular potential of a single-well type, promoting short-range attraction and long-range repulsion for better biological consistency. Both equations are subject to suitable reaction terms which model proliferation and nutrient consumption. Chemotactic effects are also taken into account. Adding an elliptic regularisation, depending on a suitable relaxation parameter, 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 the relaxation parameter go to zero, and we recover the existence of a weak solution to the original system. |
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