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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