On a relaxed Cahn-Hilliard tumour growth model with single-well potential and degenerate mobility
Résumé
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. 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 relaxation parameter δ > 0, 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 δ go to zero, and we recover the existence of a weak solution to the original system.
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