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two-variable ionic models

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Optimal control of the bidomain system (III): Existence ofminimizers and first-order optimality conditions
Karl Kunisch, Marcus Wagner
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 4 / July 2013

Published online by Cambridge University Press:

13 June 2013, pp. 1077-1106

Print publication:

July 2013
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We consider optimal control problems for the bidomain equations of cardiacelectrophysiology together with two-variable ionic models, e.g. theRogers–McCulloch model. After ensuring the existence of global minimizers, we provide arigorous proof for the system of first-order necessary optimality conditions. The proof isbased on a stability estimate for the primal equations and an existence theorem for weaksolutions of the adjoint system.