Speaker
Thomas Eiter
Description
We study the compressible Euler equations on the real line subject to frictional damping. We assume that the velocity vanishes at spatial infinity, and for the density we prescribe two positive limit values. If these values coincide, solutions convergence to a constant state in the long-time limit. However, in the case of different limit values, there is no convergence towards a steady-state, and the long-time behavior is more involved. For its study, we first transform the system into parabolic scaling variables and derive a relative-entropy inequality. In the end, we show convergence of the density towards a unique self-similar solution to the porous medium equation, while the limit velocity is determined by Darcy's law.
