On the Gevrey well-posedness of the Kirchhoff equation

TL;DR

This paper proves the almost global solvability of the Kirchhoff equation in Gevrey spaces, extending results to initial-boundary value problems in bounded and exterior domains with compact boundaries.

Contribution

It establishes almost global well-posedness for the Kirchhoff equation in Gevrey spaces, including boundary value problems in various domain types.

Findings

Almost global solvability in Gevrey spaces

Extension to bounded and exterior domains

Results applicable to initial-boundary value problems

Abstract

This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space $\gamma^s_{\eta,L^2}$. Furthermore, similar results are obtained for the initial-boundary value problems in bounded domains and in exterior domains with compact boundary.