Stability of traveling waves for doubly nonlinear equations

Seis, Christian; Winkler, Dominik

Zusammenfassung

We investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive regularity estimates for arbitrary derivatives of the solution’s pressure by extending existing results for the porous medium equation; see Kienzler (2016).