Optimal control of convective FitzHugh-Nagumo equation

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2017-05-01

Author

Uzunca, Murat
Kucukseyhan, Tugba
Yücel, Hamdullah
Karasözen, Bülent

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We investigate smooth and sparse optimal control problems for convective FitzHugh Nagumo equation with traveling wave solutions in moving excitable media. The cost function includes distributed space time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several numerical results are presented for the control of the traveling waves. We also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing Tikhonov regularization parameter. Further, we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced Hessian.

Subject Keywords

FitzHugh-Nagumo equation, Traveling waves, Sparse controls, Second order optimality conditions, Discontinuous Galerkin method

URI

https://hdl.handle.net/11511/32645

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2017.02.028

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. Uzunca, T. Kucukseyhan, H. Yücel, and B. Karasözen, “Optimal control of convective FitzHugh-Nagumo equation,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 2151–2169, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32645.