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Dispersive type estimates for fourier integrals and applications to hyperbolic systems

Pages: 1263 - 1270, Issue Special, September 2011

 Abstract        Full Text (354.7K)              

Michael Ruzhansky - Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom (email)
Jens Wirth - Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom (email)

Abstract: 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:  Fourier integrals, dispersive estimates, hyperbolic Cauchy problems
Mathematics Subject Classification:  Primary: 35B45; Secondary: 35L05, 35L45

Received: June 2010;      Revised: January 2011;      Published: October 2011.