CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Modern theory of partial differential equations

Code Completion Credits Range Language
01PDE Z,ZK 4 2P+1C Czech
Garant předmětu:
Matěj Tušek
Lecturer:
Matěj Tušek
Tutor:
Matěj Tušek
Supervisor:
Department of Mathematics
Synopsis:

1. Sobolev spaces.

2. Definition, completeness, examples.

3. Continuous and compact embedding theorems.

4. Trace theorem.

5. Weak solution (importance, derivation of the weak formulation).

6. Elliptic PDE of Second Order.

7. Existence and uniqueness of weak solutions (Lax-Milgram theorem).

8. Regularity of weak solutions.

9. Relation to the calculus of variations, Poincaré inequality.

10. Maximum principle for classical and weak solutions.

Requirements:
Syllabus of lectures:

1. Sobolev spaces.

2. Definition, completeness, examples.

3. Continuous and compact embedding theorems.

4. Trace theorem.

5. Weak solution (importance, derivation of the weak formulation).

6. Elliptic PDE of Second Order.

7. Existence and uniqueness of weak solutions (Lax-Milgram theorem).

8. Regularity of weak solutions.

9. Relation to the calculus of variations, Poincaré inequality.

10. Maximum principle for classical and weak solutions.

Syllabus of tutorials:
Study Objective:
Study materials:

Povinná literatura

1. L. C. Evans: Partial Differential Equations, 2nd ed., American Mathematical Society, Rhode Island, 2010.

Doporučená literatura

2. M. H. Protter, H. F. Weinberger: Maximum Principles in Differential Equations, Springer, New York, 1984.

3. D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.

4. R. A. Adams: Sobolev Spaces, Academic Press, New York, 2003.

5. G. Leoni: A first course in Sobolev spaces, AMS, 2017.

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-12
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6423606.html