Measure optimal controls for models inspired by biology. (English) Zbl 1517.35231
Summary: The paper is concerned with optimal control problems for a parabolic system, coupled with zero Neumann boundary conditions and with nonlinear source terms. Inspired by applications in biology and medicine, the system aims to describe two species in competition in the same spatial region and is supplemented with measure valued distributed controls, acting as source terms. Introducing general cost functionals, one can study optimal control problems. We prove the existence of solutions for the parabolic equations with measure valued controls, together with suitable stability estimates. Moreover, the existence of optimal solutions in a distributional sense is also established.
MSC:
| 35Q93 | PDEs in connection with control and optimization |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49N25 | Impulsive optimal control problems |
| 49N90 | Applications of optimal control and differential games |
| 35B35 | Stability in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 92D25 | Population dynamics (general) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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