Optimal control of convective FitzHugh–Nagumo equation

Optimal control of convective FitzHugh-Nagumo equation

We investigate smooth and sparse optimal control problems for convective FitzHughNagumo equation with travelling 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 ...

Optimal distributed control of a nonlocal convective Cahn–Hilliard equation by the velocity in 3D

In this paper we study a distributed optimal control problem for a nonlocal convective Cahn–Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system o...

Optimal Control of the b-family Equation

Abstract: This paper studies the problem of optimal control of the b-family equation. Result existence and uniqueness of weak solution in the interval to the b-family equation. According to variational inequality, optimal control theories and distributed parameter system control theories, it is proved that in the special Banach space, the norm of solution is related to the control item and init...

The discrete Riccati equation of optimal control

The convective Cahn-Hilliard equation

We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...