Travelling waves in a Fisher-Kolmogorov-type model with degenerate diffusion and nonsmooth reaction
Abstract:
We will discuss the existence and uniqueness of monotone travelling waves connecting the equilibrium states +-1.
They can either only approach these equilibria at +-infinity, or else attain them at finite points, depending on the interaction between the degenerate / singular diffusion and the nonsmooth reaction function. Then we discuss the approach to such travelling waves by solutions with rather general initial data that are sqeezed between two travelling waves (that are each other's shift).
07.01.14
09:00
László Székelyhidi
( Universität Leipzig )
Weak solutions of the Euler equations: non-uniqueness and dissipation
Abstract:
There are two aspects of weak solutions of the incompressible Euler equations which are strikingly different to the behaviour of classical solutions. Weak solutions are not unique in general and do not have to conserve the energy. Although the relationship between these two aspects is not clear, both seem to be in vague analogy with Gromov’s h-principle. In the talk I will explore this analogy in light of recent results concerning both the non-uniqueness, the search for selection criteria, as well as the dissipation anomaly and the conjecture of Onsager.
CZ
