NDLI: On the optimal control of the Schlögl-model

Content Provider	Springer Nature Link
Author	Buchholz, Rico Engel, Harald Kammann, Eileen Tröltzsch, Fredi
Copyright Year	2013
Abstract	Optimal control problems for a class of 1D semilinear parabolic equations with cubic nonlinearity are considered. This class is also known as the Schlögl model. Main emphasis is laid on the control of traveling wave fronts that appear as typical solutions to the state equation.The well-posedness of the optimal control problem and the regularity of its solution are proved. First-order necessary optimality conditions are established by standard adjoint calculus. The state equation is solved by the implicit Euler method in time and a finite element technique with respect to the spatial variable. Moreover, model reduction by Proper Orthogonal Decomposition is applied and compared with the numerical solution of the full problem. To solve the optimal control problems numerically, the performance of different versions of the nonlinear conjugate gradient method is studied. Various numerical examples demonstrate the capacities and limits of optimal control methods.
Starting Page	153
Ending Page	185
Page Count	33
File Format	PDF
ISSN	09266003
Journal	Computational Optimization and Applications
Volume Number	56
Issue Number	1
e-ISSN	15732894
Language	English
Publisher	Springer US
Publisher Date	2013-03-16
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Schlögl model Semilinear parabolic equation Travelling wave front Optimal control Model reduction Optimization Operations Research, Management Science Operations Research/Decision Theory Statistics Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Computational Mathematics

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