On some hyperbolic equations of third order

TL;DR

This paper establishes conditions under which third order hyperbolic equations with time-dependent coefficients have well-posed solutions in smooth function spaces, advancing understanding of their mathematical properties.

Contribution

It provides new sufficient conditions ensuring the well-posedness of third order hyperbolic equations with variable coefficients.

Findings

Sufficient conditions for well-posedness in $\\mathcal{C}^\\infty$

Applicability to equations with time-dependent coefficients

Enhanced understanding of third order hyperbolic equations

Abstract

We give sufficient conditions for the well-posedness in $\mathcal{C}^\infty$ of the Cauchy problem for third order equations with time dependent coefficients.