Optimal control of a class of reaction–diffusion systems

Eduardo Casas (), Christopher Ryll () and Fredi Tröltzsch ()
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Eduardo Casas: Universidad de Cantabria
Christopher Ryll: Technische Universität Berlin
Fredi Tröltzsch: Technische Universität Berlin

Computational Optimization and Applications, 2018, vol. 70, issue 3, No 2, 677-707

Abstract: 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.

Keywords: Optimal control; Reaction diffusion equations; Pointwise control constraints; Pointwise state constraints; Necessary optimality conditions; Propagating spot solutions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-018-9986-1

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