Stability of traveling waves for doubly nonlinear equations

Abstract

In this note, 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 (Ref. 15).

arXiv commentThis version includes extended proofs with additional details. Revised version

References in corpus (2)

• The thin film equation close to self-similarity
• Asymptotics near extinction for nonlinear fast diffusion on a bounded domain