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 optimization, bidomain equations, two-variable ionic models, weak local minimizer, existence theorem, necessary optimality conditions, pointwise minimum condition
@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 },
pages = {1077--1106},
year = {2013},
publisher = {EDP Sciences},
volume = {47},
number = {4},
doi = {10.1051/m2an/2012058},
mrnumber = {3082290},
zbl = {1275.49005},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2012058/}
}
TY - JOUR AU - Kunisch, Karl AU - Wagner, Marcus TI - Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1077 EP - 1106 VL - 47 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2012058/ DO - 10.1051/m2an/2012058 LA - en ID - M2AN_2013__47_4_1077_0 ER -
%0 Journal Article %A Kunisch, Karl %A Wagner, Marcus %T Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1077-1106 %V 47 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2012058/ %R 10.1051/m2an/2012058 %G en %F 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 , Direct and inverse modeling of the cardiovascular and respiratory systems. Numéro spécial, Tome 47 (2013) no. 4, pp. 1077-1106. doi: 10.1051/m2an/2012058
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