A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911197990748160 |
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| author | Cavalleri, Giulia |
| author_facet | Cavalleri, Giulia |
| contents | We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn-Hilliard type equation that describes the phase separation process between healthy and tumour tissue coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of forces, including inertial and viscous effects. The main novelty of this work is the introduction of cellular damage, whose evolution is ruled by a parabolic differential inclusion. In this paper, we prove a global-in-time existence result for weak solutions by passing to the limit in a time-discretised and regularised version of the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage Cavalleri, Giulia Analysis of PDEs 35A01, 35K35, 35K57, 35K92, 35Q74, 35Q92, 74A45 We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn-Hilliard type equation that describes the phase separation process between healthy and tumour tissue coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of forces, including inertial and viscous effects. The main novelty of this work is the introduction of cellular damage, whose evolution is ruled by a parabolic differential inclusion. In this paper, we prove a global-in-time existence result for weak solutions by passing to the limit in a time-discretised and regularised version of the system. |
| title | A phase field model of Cahn-Hilliard type for tumour growth with mechanical effects and damage |
| topic | Analysis of PDEs 35A01, 35K35, 35K57, 35K92, 35Q74, 35Q92, 74A45 |
| url | https://arxiv.org/abs/2409.14817 |