Sabine Hittmeir (RICAM Linz): Travelling waves for a nonlocal (KdV-) Burgers equation
Monday, 09.02.2015 14:15
Abstract: In this talk existence results for travelling wave solutions to a Korteweg-de-Vries-Burgers type of equation with a nonlocal diffusion term corresponding to a fractional differential operator of order between 1 and 2 are presented. This equation arises from formal asymptotic expansions for a shallow water flow associated to the triple-deck theory.
We first demonstrate the regularising effect of the fractional differential operator by deriving existence and monotonicity properties for the travelling wave solutions to the nonlinear nonlocal conservation law in the absence of the dispersive term.
As it is the case for the classical KdV-Burgers equation, travelling waves for the fractional KdV-Burgers equation are then in general not monotone, which requires a more complicated existence proof.