Pavol Brunovský

Connecting orbits in scalar reaction diffusion equations

We consider the flow of a one-dimensional reaction diffusion equation

Regular synthesis for the linear-quadratic optimal control problem with linear control constraints

{u_t} = {u_{xx}} + f(u),x \in (0,1)

The attractor of the scalar reaction diffusion equation is a smooth graph

(1.1) with Dirichlet boundary conditions

Optimal catalyst pellet activity distributions for deactivating systems

u(t,0) = u(t,1) = 0{\text{ }}

Optimal Control, Dichotomy, and Closed Range

(1.2) Let v, w denote stationary, i.e. t-independent solutions. We say that v connects to w, if there exists an orbit u(t, x) of (1.1), (1.2) such that