Dispersive type estimates for fourier integrals and applications to hyperbolic systems

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2011, 2011(Special): 1263-1270. doi: 10.3934/proc.2011.2011.1263

Dispersive type estimates for fourier integrals and applications to hyperbolic systems

Michael Ruzhansky ^1, and Jens Wirth ^1,

1.	Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom, United Kingdom

Received June 2010 Revised January 2011 Published October 2011

Abstract
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In this note we announce dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multidimensional van der Corput lemma due to the rst author.
Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.

Keywords: dispersive estimates, Fourier integrals, hyperbolic Cauchy problems.

Mathematics Subject Classification: Primary: 35B45; Secondary: 35L05, 35L45.

Citation: Michael Ruzhansky, Jens Wirth. Dispersive type estimates for fourier integrals and applications to hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 1263-1270. doi: 10.3934/proc.2011.2011.1263

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