Optimal control of a class of reaction-diffusion systems

被引：10

作者：

Casas, Eduardo ^{[1
]}

Ryll, Christopher ^{[2
]}

Troeltzsch, Fredi ^{[2
]}

机构：

[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, E-39005 Santander, Spain

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2018年 / 70卷 / 03期

关键词：

Optimal control; Reaction diffusion equations; Pointwise control constraints; Pointwise state constraints; Necessary optimality conditions; Propagating spot solutions; SPARSE OPTIMAL-CONTROL; PONTRYAGINS PRINCIPLE; BOUNDARY CONTROL; STATE; PATTERNS; SCHLOGL;

D O I：

10.1007/s10589-018-9986-1

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：677 / 707

页数：31

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