Geodesic
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

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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.

DOI : 10.1051/m2an/2012058
Classification : 35G31, 35Q92, 49J20, 49K20, 92C30
Keywords: PDE constrained optimization, bidomain equations, two-variable ionic models, weak local minimizer, existence theorem, necessary optimality conditions, pointwise minimum condition 
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     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},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {4},
     year = {2013},
     doi = {10.1051/m2an/2012058},
     mrnumber = {3082290},
     zbl = {1275.49005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012058/}
}
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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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