Special topics numerical analysis: Monotone operators in nonlinear PDEs

 

Topics:

• Monotone operators
• Theorem of Browder-Minty
• Quasilinear elliptic equations
• Pseudomonotone operators
• Evolution problems 
• Maximal monotone operators

Lecture Notes: Download

Handwritten notes: Download
 

Date	Time	Room	Lecture	Exercises
2023-10-04	08:30	S2 416-1	Monotone operators, Minty's trick
2023-10-11	08:30	S2 416-1	Theorem of Browder-Minty I
2023-10-18	10:15	S2 346	Theorem of Browder-Minty II	Exercise #1
2023-10-25	10:15	S2 346	Nemyckii operators	Solution #1
2023-11-08	10:15	S2 346	Quasilinear elliptic PDEs	Exercise #2
2023-11-15	10:15	S2 346	Pseudomonotone operators	Solution #2
2023-11-22	10:15	S2 346	Brezis existence theorem	Exercise #3
2023-11-29	10:15	S2 346	Stationary Navier-Stokes equations	Solution #3
2023-12-06	10:15	S2 346	De Rham lemma
2023-12-13	10:15	S2 346	Applications
2024-01-10	10:15	S2 346	Applications
2024-01-17	10:15	S2 346	Evolutionary problems
2024-01-24	10:15	S2 346	Bochner spaces
2024-01-31	10:15	S2 346	Proof of the Aubin-Lions lemma

Literature:

• R. E. Showalter. Monotone Operators in Banach Space and Nonlinear Partial Differential Equations.
• M. Galewski. Basic Monotonicity Methods with Some Applications.
• M. Růžička. Nichtlineare Funktionalanalysis.
• V. Barbu. Nonlinear Differential Equations of Monotone Types in Banach Spaces.