The talk **On bounded solutions to the compressible isentropic Euler system**, by Ondřej Kreml, will be held on Monday May 19, 2014 at 8:30 in room K4. After that, Marek Netušil will talk about his recent work with a presentation entitled **Mathematical modelling of an arterial wall**.

**Abstract of the talk**

We consider the compressible isentropic Euler system in the whole space $\mathbb{R}^2$. Using the tools developed by De Lellis and Székelyhidi for incompressible Euler system we first prove that there exist Lipschitz initial data for which there exist infinitely many bounded admissible weak solutions. The proof is based on the analysis of the Riemann problem for the Euler system. Further study of the Riemann problem shows that for every Riemann initial data yielding the self-similar solution in the form of two admissible shocks there exist in fact infinitely many admissible bounded weak solutions. Moreover for some of these initial data such solutions dissipate more total energy than the self-similar solution which might be looked at as a natural candidate for the "physical" solution. Finally, we show that self-similar solutions consisting only of rarefaction waves are unique in the class of bounded admissible weak solutions.

**Abstract of the PhD presentation**

Cardiovascular diseases are one of the most common causes of death worldwide. Thus, understanding the blood vessels functionality is of crucial importance. The presentation is focused on the mathematical description of elastic arteries. Often used models will be presented and their capabilities will be discussed.