(in Polish) Hiperboliczne prawa zachowania 1000-1M20HPZ
Analysis of hyperbolic conservation laws is probably one of the most difficult problems in modern theory of partial differential equations. Although they are ubiquitous in applications, their general mathematical theory is far from complete. Current results can only cover very specific cases (small initial data, scalar equation etc).
We start the lecture from presenting particular models and their application. Then, we focus our attention on mathematical analysis of the models (existence of solutions, uniqueness, asymptotic behaviour).
In particular, we plan to cover the following topics:
1. Existence and uniqueness for the Cauchy problem for scalar conservation laws in the class of weak entropy solutions
2. Compensated compactness methods for hyperbolic conservation laws.
3. Standard Riemann semigroup technique.
If time permits, the following may be discussed during lectures or tutorials:
4. Relative entropy method and long-time asymptotics.
5. Kinetic formulation of conservation laws and applications to singular limits.
6. Conservation of energy and regularity of solutions, Onsager’s conjecture.
Type of course
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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