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

Karl Kunisch; Marcus Wagner

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 4, page 1077-1106
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Kunisch, Karl, and 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 47.4 (2013): 1077-1106. <http://eudml.org/doc/273184>.

@article{Kunisch2013,
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.},
author = {Kunisch, Karl, Wagner, Marcus},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {PDE constrained optimization; bidomain equations; two-variable ionic models; weak local minimizer; existence theorem; necessary optimality conditions; pointwise minimum condition; bidomain system; existence results},
language = {eng},
number = {4},
pages = {1077-1106},
publisher = {EDP-Sciences},
title = {Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions},
url = {http://eudml.org/doc/273184},
volume = {47},
year = {2013},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 4
SP - 1077
EP - 1106
AB - 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.
LA - eng
KW - PDE constrained optimization; bidomain equations; two-variable ionic models; weak local minimizer; existence theorem; necessary optimality conditions; pointwise minimum condition; bidomain system; existence results
UR - http://eudml.org/doc/273184
ER -

References

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