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Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects
- Source :
- SIAM Journal on Control and Optimization. 59:1555-1580
- Publication Year :
- 2021
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2021.
-
Abstract
- In this paper, we study an optimal control problem for a macroscopic mechanical tumour 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 minimise a cost functional involving mechanical stresses. Special attention is given to sparsity effects, where with the inclusion of convex non-differentiable regularisation 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.<br />26 pages
- Subjects :
- 0209 industrial biotechnology
Control and Optimization
Field (physics)
Sparse optimal control
Mathematics::Analysis of PDEs
Phase (waves)
02 engineering and technology
01 natural sciences
Cahn-Hilliard equation
Physics::Fluid Dynamics
020901 industrial engineering & automation
FOS: Mathematics
Tumor growth
Linear elasticity
0101 mathematics
Cahn–Hilliard equation
Mathematics - Optimization and Control
49J20, 49K20, 35K57, 74B05, 35Q92
Nonlinear Sciences::Pattern Formation and Solitons
Mathematics
Optimality conditions
Mechanical effects
Applied Mathematics
010102 general mathematics
Mathematical analysis
Nonlinear Sciences::Cellular Automata and Lattice Gases
Optimal control
Optimization and Control (math.OC)
Elliptic-parabolic system
Subjects
Details
- ISSN :
- 10957138 and 03630129
- Volume :
- 59
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Control and Optimization
- Accession number :
- edsair.doi.dedup.....1b49e76cabdd906f8f3d5325d9e8092e