Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects

Harald Garcke, Kei Fong Lam, Andrea Signori

Research output: Contribution to journalJournal articlepeer-review

12 Citations (Scopus)
19 Downloads (Pure)


In this paper, we study an optimal control problem for a macroscopic mechanical tumor model based on the phase field approach. The model couples a Cahn--Hilliard-type equation to a system of linear elasticity and a reaction-diffusion equation for a nutrient concentration. By taking advantage of previous analytical well-posedness results established by the authors, we seek optimal controls in the form of a boundary nutrient supply as well as concentrations of cytotoxic and antiangiogenic drugs that minimize a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex nondifferentiable regularization terms to the cost functional, we can infer from the first-order optimality conditions that the optimal drug concentrations can vanish on certain time intervals.

Original languageEnglish
Pages (from-to)1555-1580
Number of pages26
JournalSIAM Journal on Control and Optimization
Issue number2
Publication statusPublished - 15 Apr 2021

Scopus Subject Areas

  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Cahn-Hilliard equation
  • Elliptic-parabolic system
  • Linear elasticity
  • Mechanical effects
  • Optimality conditions
  • Sparse optimal control
  • Tumor growth


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