Titelaufnahme

Titel
Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - a monolithic approach.
Verfasser/ VerfasserinKunisch, Karl ; Pieper, Konstantin ; Rund, Armin
Erschienen in
ESAIM: Mathematical Modelling and Numerical Analysis, 2016, Jg. 50, H. 2, S. 381-414
ErschienenEDP Sciences, 2016
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Time optimal control / monodomain equations / semismooth Newton method / reaction diffusion system / asymptotic behavior
ISSN1290-3841
URNurn:nbn:at:at-ubg:3-3526 Persistent Identifier (URN)
DOI10.1051/m2an/2015048 
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Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - a monolithic approach. [1.95 mb]
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Zusammenfassung (Englisch)

Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the RogersMcCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.