| Issue |
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
Direct and inverse modeling of the cardiovascular and respiratory systems
|
|
|---|---|---|
| Page(s) | 1077 - 1106 | |
| DOI | https://doi.org/10.1051/m2an/2012058 | |
| Published online | 13 June 2013 | |
Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions
1 University of Graz, Institute for
Mathematics and Scientific Computing, Heinrichstraße 36, 8010
Graz,
Austria.
karl.kunisch@uni-graz.at
2 University of Leipzig, Department of
Mathematics, P. O. B. 10 09
20, 04009
Leipzig,
Germany.
www.thecitytocome.de/marcus.wagner@math.uni-leipzig.de
Received:
27
December
2011
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.
Mathematics Subject Classification: 35G31 / 35Q92 / 49J20 / 49K20 / 92C30
Key words: PDE constrained optimization / bidomain equations / two-variable ionic models / weak local minimizer / existence theorem / necessary optimality conditions / pointwise minimum condition
© EDP Sciences, SMAI, 2013
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