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Optimal Control of a Class of Reaction-Diffusion Systems with Pointwise State Constraints

  • Eduardo Casas
  • Konstantinos Chrysafinos
  • Mariano Mateos
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Abstract

We study optimal control problems governed by a system of semilinear reaction-diffusion equations. The assumptions on the governing system are formulated so that our results apply to several models, including the Brusselator, Schnakenberg, and Gray--Scott systems. We prove the existence and uniqueness of a solution to the governing system without imposing any non-negativity assumption on the data. This allows us to study unconstrained, control-constrained, and state-constrained optimal control problems. For all these problems, we derive first-order necessary and second-order sufficient optimality conditions. The control acts on the activator equation through the boundary. Numerical examples demonstrate that both the inhibitor and the activator can be efficiently controlled.

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Cite

BibTeXRIS
BibTeX
@misc{casas2026optimal,
  title = {{Optimal Control of a Class of Reaction-Diffusion Systems with Pointwise State Constraints}},
  author = {Eduardo Casas and Konstantinos Chrysafinos and Mariano Mateos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08114},
  eprint = {2610.08114},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08114},
}
RIS
TY  - UNPB
TI  - Optimal Control of a Class of Reaction-Diffusion Systems with Pointwise State Constraints
AU  - Eduardo Casas
AU  - Konstantinos Chrysafinos
AU  - Mariano Mateos
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08114
UR  - https://arxiv.org/abs/2610.08114
AB  - We study optimal control problems governed by a system of semilinear reaction-diffusion equations. The assumptions on the governing system are formulated so that our results apply to several models, including the Brusselator, Schnakenberg, and Gray--Scott systems. We prove the existence and uniqueness of a solution to the governing system without imposing any non-negativity assumption on the data. This allows us to study unconstrained, control-constrained, and state-constrained optimal control problems. For all these problems, we derive first-order necessary and second-order sufficient optimality conditions. The control acts on the activator equation through the boundary. Numerical examples demonstrate that both the inhibitor and the activator can be efficiently controlled.
ER  -