On t-dependent hyperbolic systems. Part 2

TL;DR

This paper develops an abstract framework to analyze the large-time asymptotic behavior of solutions to hyperbolic equations with time-dependent coefficients, using diagonalization and asymptotic integration techniques.

Contribution

It introduces a novel abstract approach for deriving large-time asymptotics of hyperbolic systems with time-dependent coefficients.

Findings

Framework successfully characterizes asymptotic behavior for large times

Applicable to generic hyperbolic systems with time-dependent coefficients

Provides a basis for further analysis of hyperbolic PDEs with variable coefficients

Abstract

We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the large-time asymptotics is of hyperbolic type. Our approach is based on diagonalisation procedures combined with asymptotic integration arguments.