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Optimal control of a class of reaction–diffusion systems

Author

Listed:
  • Eduardo Casas

    (Universidad de Cantabria)

  • Christopher Ryll

    (Technische Universität Berlin)

  • Fredi Tröltzsch

    (Technische Universität Berlin)

Abstract

The optimal control of a system of nonlinear reaction–diffusion equations is considered that covers several important equations of mathematical physics. In particular equations are covered that develop traveling wave fronts, spiral waves, scroll rings, or propagating spot solutions. Well-posedness of the system and differentiability of the control-to-state mapping are proved. Associated optimal control problems with pointwise constraints on the control and the state are discussed. The existence of optimal controls is proved under weaker assumptions than usually expected. Moreover, necessary first-order optimality conditions are derived. Several challenging numerical examples are presented that include in particular an application of pointwise state constraints where the latter prevent a moving localized spot from hitting the domain boundary.

Suggested Citation

  • Eduardo Casas & Christopher Ryll & Fredi Tröltzsch, 2018. "Optimal control of a class of reaction–diffusion systems," Computational Optimization and Applications, Springer, vol. 70(3), pages 677-707, July.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:3:d:10.1007_s10589-018-9986-1
    DOI: 10.1007/s10589-018-9986-1
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    References listed on IDEAS

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    1. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 153-185, September.
    2. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "Erratum to: On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 187-188, September.
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    Cited by:

    1. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2024. "Epidemic outbreaks and the optimal lockdown area: a spatial normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 349-411, February.

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