Knopf, Patrik and Signori, Andrea (2022) Existence of weak solutions to multiphase Cahn-Hilliard-Darcy and Cahn-Hilliard-Brinkman models for stratified tumor growth with chemotaxis and general source terms. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 47 (2). pp. 233-278. ISSN 0360-5302, 1532-4133
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We investigate a multiphase Cahn-Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the tumor. Compared to classical two-phase tumor growth models, the multiphase model can be used to describe a stratified tumor exhibiting several layers of tissue (e.g., proliferating, quiescent and necrotic tissue) more precisely. Our model consists of a convective Cahn-Hilliard type equation to describe the tumor evolution, a velocity equation for the associated volume-averaged velocity field, and a convective reaction-diffusion type equation to describe the density of the chemical species. The velocity equation is either represented by Darcy's law or by the Brinkman equation. We first construct a global weak solution of the multiphase Cahn-Hilliard-Brinkman model. After that, we show that such weak solutions of this system converge to a weak solution of the multiphase Cahn-Hilliard-Darcy system as the viscosities tend to zero in some suitable sense. This means that the existence of a global weak solution to the Cahn-Hilliard-Darcy system is also established.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; FREE-BOUNDARY PROBLEMS; SINGULAR POTENTIALS; MATHEMATICAL-MODEL; TREATMENT TIME; SYSTEM; SIMULATION; INVASION; FLOWS; Brinkman's law; Cahn-Hilliard equation; Chemotaxis; Darcy's law; Limit of vanishing viscosities; Multiphase model; Tumor growth |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Jul 2022 09:48 |
| Last Modified: | 28 Jul 2022 09:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46148 |
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