Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type
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| Format: | Preprint |
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2026
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| _version_ | 1866909011212763136 |
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| author | Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta |
| author_facet | Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta |
| contents | We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system 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. Chemotaxis and active transport effects are taken into account, and hyperthermia appears as a control variable. We introduce a suitable tracking-type cost functional and show the existence of optimal controls. Then, we analyse the differentiability of the control-to-state operator and establish necessary first-order conditions expressed through a variational inequality involving the adjoint state variables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type Cavalleri, Giulia Colli, Pierluigi Rocca, Elisabetta Optimization and Control Analysis of PDEs 35Q93, 49J20, 49K20, 35Q92, 92C50 We study a distributed optimal control problem for a nonisothermal Caginalp-type phase-field model that describes tumour growth under thermal therapy. The PDE system 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. Chemotaxis and active transport effects are taken into account, and hyperthermia appears as a control variable. We introduce a suitable tracking-type cost functional and show the existence of optimal controls. Then, we analyse the differentiability of the control-to-state operator and establish necessary first-order conditions expressed through a variational inequality involving the adjoint state variables. |
| title | Optimal control for a fourth-order nonisothermal tumor growth model of Caginalp type |
| topic | Optimization and Control Analysis of PDEs 35Q93, 49J20, 49K20, 35Q92, 92C50 |
| url | https://arxiv.org/abs/2604.24108 |