Nonlinear Differential Equations (NMNV406) (Summer Semester 2023/2024)
This lecture course will cover the solution of nonlinear differential equations. Topics covered will include:
- Basic theorems from the theory of monotone and potential operators,
- Nonlinear differential equations in divergent form,
- Carathéodory's growth conditions, Nemycky operators,
- Variational methods and application of theory of monotone and potential operator, and proof of existence of solution,
- Numerical solution of nonlinear differential equations using the finite element method.
Exams:
The final exam will consist of a 30 minute oral examination on the topics covered.
Lectures:
- Wednesday 12:20 – 13:50, K433KNM Sokolovská 83 Karlín
- Lecture Notes:
Practicals:
- Wednesday 14:00 – 15:30, K433KNM Sokolovská 83 Karlín
- Practical 0: Exercises
- Practical 1: Exercises; Solutions
- Practical 2: Exercises; Solutions
- Practical 3: Exercises; Solutions
- Practical 4: Exercises; Solutions
- Practical 5: Exercises; Solutions
- Practical 6: Exercises
- Practical 7: Exercises; Solutions
- Practical 8: Exercises; Solutions
Suggested Reading:
- K. Böhmer, Numerical Methods for Nonlinear Elliptic Differential Equations, Oxford University Press, 2010.
- V. Dolejší & K. Najzar, Nelineární funkcionální analýza, matfyzpress, 2011.
- E. Ziedler. Nonlinear functional analysis and its applications I, Springer, 1984.
- E. Ziedler. Nonlinear functional analysis and its applications II/A, Springer, 1990.
- J. Nečas. Introduction to the Theory of Nonlinear Elliptic Equations, Wiley, 1986
- L. C. Evans, Partial Differential Equations, AMS, 2010.