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arXiv · 2603.14960

Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential

Pierluigi Colli·Elisabetta Rocca·Jürgen Sprekels
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Abstract

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.

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Pierluigi Colli, Elisabetta Rocca, Jürgen Sprekels. 2026-03-16. Optimal control of a tumor growth model with hyperbolic relaxation of the chemical potential. https://arxiv.org/abs/2603.14960

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