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Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions

Published online by Cambridge University Press:  13 June 2013

Karl Kunisch  and
Marcus Wagner
Karl Kunisch
Affiliation:
University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstraße 36, 8010 Graz, Austria.. karl.kunisch@uni-graz.at
Marcus Wagner
Affiliation:
University of Leipzig, Department of Mathematics, P. O. B. 10 09 20, 04009 Leipzig, Germany.; www.thecitytocome.de/marcus.wagner@math.uni-leipzig.de
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Abstract

We consider optimal control problems for the bidomain equations of cardiac electrophysiology together with two-variable ionic models, e.g. the Rogers–McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions. The proof is based on a stability estimate for the primal equations and an existence theorem for weak solutions of the adjoint system.

Keywords

PDE constrained optimizationbidomain equationstwo-variable ionic modelsweak local minimizerexistence theoremnecessary optimality conditionspointwise minimum condition
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 1077 - 1106
Copyright
© EDP Sciences, SMAI, 2013

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