A class of non-analytic functions for the global solvability of Kirchhoff equation

TL;DR

This paper extends the class of initial data for which the Kirchhoff equation is globally solvable, moving from Sobolev to ultradifferentiable classes, and proves global existence for large data.

Contribution

It introduces a broader class of functions, extending Manfrin's class within ultradifferentiable spaces, and establishes global solvability for the Kirchhoff equation with large initial data.

Findings

Proved global solvability in wider function classes.

Extended Manfrin's class to ultradifferentiable spaces.

Achieved global existence results for large data.

Abstract

We consider the global solvability to the Cauchy problem of Kirchhoff equation with generalized classes of Manfrin's class. Manfrin's class is a subclass of Sobolev space, but we shall extend this class as a subclass of the ultradifferentiable class, and we succeed to prove the global solvability of Kirchhoff equation with large data in wider classes from the previous works.