On control problems for some advection-reaction-diffusion systems

The present article is concerned with the Neumann boundary control of systems modeled by parabolic equations of advection-reaction-diffusion type with a particular emphasis on systems which are unstable if uncontrolled. To solve these problems we use a combination of finite difference methods for the time discretization, finite element methods for the space discretization and conjugate gradient algorithms for the iterative solution of the discrete control problems. We then apply the above methodology to the solution of test problems in two-dimensions, including problems related to nonlinear models.