Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912967822409728 |
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| author | Colli, Pierluigi Rocca, Elisabetta Sprekels, Jürgen |
| author_facet | Colli, Pierluigi Rocca, Elisabetta Sprekels, Jürgen |
| contents | In this paper, we study the optimal control of a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. Both the cases when the double-well potential governing the phase evolution is of either regular or logarithmic type are covered by the analysis. We show the Fréchet differentiability of the associated control-to-state operator in suitable Banach spaces and establish first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The necessary optimality conditions are then used to derive sparsity results for the optimal controls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14960 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential Colli, Pierluigi Rocca, Elisabetta Sprekels, Jürgen Optimization and Control Analysis of PDEs 49J20, 49K20, 49K40, 35K57, 37N25 In this paper, we study the optimal control of a phase field model for a tumor growth model of Cahn--Hilliard type in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. Both the cases when the double-well potential governing the phase evolution is of either regular or logarithmic type are covered by the analysis. We show the Fréchet differentiability of the associated control-to-state operator in suitable Banach spaces and establish first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The necessary optimality conditions are then used to derive sparsity results for the optimal controls. |
| title | Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential |
| topic | Optimization and Control Analysis of PDEs 49J20, 49K20, 49K40, 35K57, 37N25 |
| url | https://arxiv.org/abs/2603.14960 |