Dispersive estimates for hyperbolic systems with time-dependent coefficients

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.

35 pages

References in corpus (3)

• $C^m$-theory of damped wave equations with stabilisation
• Diagonalisation schemes and applications
• Global time estimates for solutions to equations of dissipative type

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• A necessary and sufficient condition on scattering for the regularly hyperbolic systems
• On t-dependent hyperbolic systems. Part 2
• Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients
• Thermo-elasticity for anisotropic media in higher dimensions
• Dispersive type estimates for Fourier integrals and applications to hyperbolic systems