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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

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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