Dispersive estimates for hyperbolic systems with time-dependent coefficients

TL;DR

This paper develops dispersive estimates for solutions to hyperbolic systems with time-dependent coefficients by diagonalising symbols and applying a multi-dimensional van der Corput lemma, advancing understanding of their behavior.

Contribution

It introduces a novel approach combining symbol diagonalisation and van der Corput lemma to derive dispersive estimates for time-dependent hyperbolic systems.

Findings

Derived dispersive estimates for hyperbolic systems with time-dependent coefficients.

Established a method for analyzing solution representations via symbol diagonalisation.

Extended dispersive analysis techniques to multi-dimensional hyperbolic systems.

Abstract

This paper is devoted to the study of time-dependent hyperbolic systems and the derivation of dispersive estimates for their solutions. It is based on a diagonalisation of the full symbol within adapted symbol classes in order to extract the essential information about representations of solutions. This is combined with a multi-dimensional van der Corput lemma to derive dispersive estimates.