Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations with weak dissipation

TL;DR

This paper studies mildly degenerate Kirchhoff equations with weak dissipation, proving global existence of solutions for small parameters and providing error estimates comparing these solutions to simpler first-order models.

Contribution

It introduces new global existence results and error estimates for mildly degenerate Kirchhoff equations with weak dissipation, expanding understanding of their long-term behavior.

Findings

Global solutions exist for small parameters

Error estimates between solutions and first-order approximations

Conditions for the existence of solutions

Abstract

We consider mildly degenerate Kirchhoff equations with a small parameter and a weak dissipation term. We prove the existence of global solutions when the parameter is small with respect to the size of initial data. Then we provide global-in-time error estimates on the difference between the solution of our problem and the solution of the corresponding first order problem.