Graduate Course on
Nonlinear Operator Semigroups
Gisèle Ruiz Goldstein, May-June 2019
The course consists of four lectures, each one lasting for two hours.
Lecture 1: Review of semigroups of linear operators, Hille-Yosida Theorem, etc. Nonlinear dissipative operators, Crandall-Liggett Theorem. Mild solutions (= limit solutions = bonne solutions) of the Cauchy problem. Benilan-Kobayashi Theorem (Linearity is irrelevant.)
Lecture 2: (Linearity is relevant.) Counterexamples, Perturbation and Approximation Theory. Full generalization of the Hille-Yosida Theorem in Hilbert spaces.
Lecture 3: Applications I: Hilbert Spaces: Subdifferentials of convex functions, Nonlinear Mean Ergodic Theorem.
Nonreflexive Spaces: First order hyperbolic problems in BUC and L1 , single conservation laws, Hamiton-Jacobi equation, viscosity solutions.
Lecture 4: Applications II: Filtration equation, Wentzell boundary conditions, Landisman-Lazer Theorem and extensions, Thomas-Fermi Theory
