Gradient Structure of Cascade Systems under Non-Autonomous Perturbations

Alexandre Nolasco de Carvalho - ICMC (USP)

Abstract:

 In this talk we present results ensuring that cascade systems with finitely many equilibria, all of them hyperbolic, are dynamically gradient and, consequently, have a Lyapunov functional. We also show that small non-autonomous perturbations of cascade systems give rise to dynamic gradient skew product semiflows with a Lyapunov functional. The theory is applied to some examples of ODEs and parabolic PDEs in dumbbell domains.