OPTIMAL CONTROL OF THE BIDOMAIN SYSTEM (III): EXISTENCE OF MINIMIZERS AND FIRST-ORDER OPTIMALITY CONDITIONS
OPTIMAL CONTROL OF THE BIDOMAIN SYSTEM (III): EXISTENCE OF MINIMIZERS AND FIRST-ORDER OPTIMALITY CONDITIONS
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DOI：
10.1051/m2an/2012058
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发表时间：
2013-07-01
影响因子：
1.9
通讯作者：
Wagner, Marcus
中科院分区：
文献类型：
--
作者：
Kunisch, Karl;Wagner, Marcus
我们考虑心脏电生理学的bidomain方程的最优控制问题，连同两个变量的离子模型，如罗杰斯-麦卡洛克模型。在保证了全局极小点的存在性之后，我们给出了一阶最优性必要条件的严格证明。证明是基于原方程的稳定性估计和伴随系统弱解的存在性定理。
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.