By studying several important models, this course will provide some fundamental tools for the analysis and the understanding of evolution partial differential equations.
Course Prerequisites
Basic concepts of functional analysis, Lebesgue integration theory and Sobolev spaces (the main results will be recalled during the course).
Teaching Methods
Lectures and Exercises
Assessment Methods
Oral Exam on the arguments of the course. The oral exam aims at verifying the level comprehension of the arguments of the course and the clarity of presentation. The final score takes into account the the depth of understanding and the clarity of presentation.
Texts
-H. Brezis, Operateurs Maximaux Monotones dans les Espaces de Hilbert, North Holland, 1973. -L.C. Evans, Partial Differential Equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, 2002. -J.C. Robinson, Infinite dimensional dynamical systems, Cambridge University Press, 2001. -S. Salsa, Partial Differential Equations in Action. Springer, 2010. -N.V. Krylov, Lectures on Elliptic and parabolic equations in Hölder spaces, AMS, 1996
Contents
We will discuss the following themes, also according to students interest: -Variational methods for linear parabolic equations -Variational methods for linear second order hyperbolic equations -Reaction diffusion equations, Cahn-Hilliard equations and applications to phase transition problems -Solvability and optimal regularity of linear parabolic equations in Hölder spaces.
