Evolutionary Partial Differential Equations

The course aims to provide the basic functional-analytic and variational tools for the study of the main classes of evolution equations, with particular emphasis on parabolic and hyperbolic problems, as well as on the Navier-Stokes equations. The course also presents models arising from applications within a rigorous mathematical framework.

At the end of the course, students will be able to analyze evolution problems in appropriate functional spaces, discuss existence, uniqueness, continuous dependence, and regularity of solutions by means of classical techniques such as the Faedo-Galerkin method and time discretization.