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
2 University of Leipzig, Department of Mathematics, P. O. B. 10 09 20, 04009 Leipzig, Germany.
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
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