Time-Periodic Fitzhugh-Nagumo Equation and the Optimal Control Problems

Abstract

In this work, the authors considered the periodic optimal control problem of Fitzhugh-Nagumo equation. They firstly prove the existence of time-periodic solution to Fitzhugh-Nagumo equation. Then they show the existence of optimal solution to the optimal control problem, and finally the first order necessary condition is obtained by constructing an appropriate penalty function.

Keywords

Fitzhugh-Nagumo equation / Time-periodic / Optimal control

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