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Domain decomposition in optimal control of partial differential equations on networked domains

Speaker: Günter Leugering

Abstract

We consider partial differential equations on networks, such as graphs or multiply linked domains. We focus on hyperbolic equations or systems of such equations and consider particularly final value optimal control problems. The point of the analysis is to decompose the corresponding optimality system in space and time such that the decomposed system is, in turn, an optimality system of a local optimal control problem in a more simple space-time domain, where standard optimal control software is applicable. Algorithms are presented on the infinite-dimensional level, well-posedness and convergence are discussed, and a posteriori error estimates with respect to the decomposition are provided. Recent applications are going to be presented.


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