Optimal Control of Convective FitzHugh-Nagumo Equation

Bülent Karasözen, Tuğba Küçükseyhan, Murat Uzunca

Published 2015-09-09Version 1

We investigate optimal control of wave propagation in a moving excitable media described by two-dimensional convective FitzHugh-Nagumo (FHN) model. The model consists of two coupled reaction diffusion convection equations describing the propagation of waves in blood coagulation. The flow plays an important role by the regularization of the excitation threshold and traveling wave propagation. Optimal control of the convective FHN equation is illustrated on two numerical examples with desired states in the whole space-time domain and at the final time. For space discretization we use the symmetric interior penalty discontinuous Galerkin (SIPG) method and for time discretization the implicit Euler method.