Stability of periodic solutions to parabolic problems with nonlinear boundary conditions

Abstract

We investigate nonautonomous quasilinear systems of parabolic partial differential equations with fully nonlinear boundary conditions. We establish local wellposedness and study the time and space regularity of the solutions. Our main results give principles of linearized (orbital) stability and instability for solutions in the vicinity of a periodic solution. Our approach relies on a detailed study of regularity properties of the linearized nonautonomous problem and its evolution family.