Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866913750082125824 |
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| author | Cavalleri, Giulia Miranville, Alain |
| author_facet | Cavalleri, Giulia Miranville, Alain |
| contents | In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca, On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage (2025)], couples a Fisher-Kolmogorov type equation for tumor cell density with a reaction-diffusion equation for the lactate, a quasi-static force balance governing the displacement, and a nonlinear differential inclusion for tissue damage. The control variables, representing chemotherapy and a lactate-targeting drug, influence tumor progression and treatment response. Starting from well-posedness, regularity, and continuous dependence results already established, we define a suitable cost functional and prove the existence of optimal controls. Then, we analyze the differentiability of the control-to-state operator and establish a necessary first-order condition for treatment optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage Cavalleri, Giulia Miranville, Alain Analysis of PDEs Optimization and Control 35Q93, 49J20, 49K20, 35Q92, 92C50 In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca, On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage (2025)], couples a Fisher-Kolmogorov type equation for tumor cell density with a reaction-diffusion equation for the lactate, a quasi-static force balance governing the displacement, and a nonlinear differential inclusion for tissue damage. The control variables, representing chemotherapy and a lactate-targeting drug, influence tumor progression and treatment response. Starting from well-posedness, regularity, and continuous dependence results already established, we define a suitable cost functional and prove the existence of optimal controls. Then, we analyze the differentiability of the control-to-state operator and establish a necessary first-order condition for treatment optimality. |
| title | Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage |
| topic | Analysis of PDEs Optimization and Control 35Q93, 49J20, 49K20, 35Q92, 92C50 |
| url | https://arxiv.org/abs/2503.17049 |