Optimal control for nonlocal reaction‐diffusion system describing calcium dynamics in cardiac cell. (14th December 2020)

• Record Type: Journal Article
• Authors: Bendahmane, Mostafa; Erraji, Elmahdi; Karami, Fahd
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 6(2021)
• Page Start: 4802
• Page End: 4834
• Publication Date: 2020-12-14
• Subjects: calcium model -- finite element method -- first order optimality conditions -- nonlocal diffusion -- numerical simulation -- optimal control -- weak solution; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7071
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The purpose of this paper is to introduce an optimal control for a nonlocal calcium dynamic model in a cardiac cell acting on ryanodine receptors. The optimal control problem is considered as a coupled nonlocal reaction‐diffusion system with a transmission boundary condition covering the sarcoplasmic reticulum and cytosolic domain. We establish the well‐posedness result of the adjoint problem using Faedo‐Galerkin approximation, a priori estimates, and compactness arguments. The numerical discretization of direct and adjoint problems is realized by using the implicit Euler method in time and the finite element for spatial discretization. Moreover, we obtain the stability result in the L 2 ‐norm for the direct and the adjoint discrete problems. Finally, in order to illustrate the control of our calcium dynamic model, we present some numerical experiments devoted to constant and nonlocal diffusions using the proposed numerical scheme.