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.
@article{M2AN_2013__47_4_1077_0,
author = {Kunisch, Karl and Wagner, Marcus},
title = {Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {1077-1106},
doi = {10.1051/m2an/2012058},
mrnumber = {3082290},
zbl = {1275.49005},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_4_1077_0}
}
Kunisch, Karl; Wagner, Marcus. Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1077-1106. doi : 10.1051/m2an/2012058. http://gdmltest.u-ga.fr/item/M2AN_2013__47_4_1077_0/
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