Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915543101997056 |
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| author | Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta |
| author_facet | Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta |
| contents | We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an equation for the heat balance, and a reaction-diffusion equation for the nutrient concentration. The resulting nonlinear system incorporates chemotaxis and active transport effects, and is supplemented with no-flux boundary conditions. The analysis is carried out through a two-step approximation procedure, involving a regularization of the potential and a Faedo-Galerkin discretization scheme. Under stronger regularity assumptions, we further establish the existence of strong solutions and their uniqueness via a continuous dependence result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta Analysis of PDEs 5K61, 35K35, 35D30, 35B65, 35A02, 35Q92, 92C50 We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an equation for the heat balance, and a reaction-diffusion equation for the nutrient concentration. The resulting nonlinear system incorporates chemotaxis and active transport effects, and is supplemented with no-flux boundary conditions. The analysis is carried out through a two-step approximation procedure, involving a regularization of the potential and a Faedo-Galerkin discretization scheme. Under stronger regularity assumptions, we further establish the existence of strong solutions and their uniqueness via a continuous dependence result. |
| title | Well-posedness for a fourth-order nonisothermal tumor growth model of Caginalp type |
| topic | Analysis of PDEs 5K61, 35K35, 35D30, 35B65, 35A02, 35Q92, 92C50 |
| url | https://arxiv.org/abs/2508.07979 |