Neumann Control of Unstable Parabolic Systems: Numerical Approach

The present article is concerned with the Neumann control of systems modeled by scalar or vector parabolic equations of reaction-advection-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 apply then the above methodology to the solution of test problems in two dimensions, including problems related to nonlinear models.