On the Analysis of Systems Described by Classes of Partial Differential Equations

We provide an algorithmic approach for the analysis of infinite dimensional systems described by partial differential equations. In particular, we look at the stability properties of a class of strongly continuous semigroups generated by nonlinear parabolic partial differential equations with appropriate boundary conditions. Our approach is based on the application of semidefinite programming to the computation of Lyapunov-type certificates defined by polynomial functions. An illustrative example is given