@article{10902/13874,
year = {2018},
month = {7},
url = {http://hdl.handle.net/10902/13874},
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.},
organization = {Eduardo Casas was partially supported by the Spanish Ministerio de Economía, Industria y Competitividad under Projects MTM2014-57531-P and MTM2017-83185-P. Christopher Ryll and Fredi Tröltzsch are supported by DFG in the framework of the Collaborative Research Center SFB 910, Project B6.},
publisher = {Springer Nature},
publisher = {Computational Optimization and Applications, 2018, 70(3),  677-707},
title = {Optimal control of a class of reaction-diffusion systems},
author = {Casas Rentería, Eduardo and Ryll, Christopher and Tröltzsch, Fredi},
}