SIAM Journal on Mathematical Analysis· 2026Q1
On a Relaxed Cahn–Hilliard Tumor Growth Model with Single-Well Potential and Degenerate Mobility
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- Q1SCImago
- 2026year
Short summary
A relaxed Cahn-Hilliard tumor growth model with degenerate mobility and a singular potential is shown to have a weak solution, with existence recovered for the original system as the relaxation parameter approaches zero.
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Key points
- A phase-field system models tumor growth using a Cahn-Hilliard equation coupled with nutrient dynamics.
- The model features degenerate mobility, a singular potential, reaction terms for proliferation/consumption, and chemotaxis.
- An elliptic regularization with a relaxation parameter is introduced to prove the existence of a weak solution for the relaxed system.
- The existence of a weak solution for the original system is recovered by letting the relaxation parameter approach zero.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. SIAM Journal on Mathematical Analysis, 2026 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics