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Estimates for Pseudo-differential and Hyperbolic Differential Equations via Fourier Integrals with Complex Phases

  • Michael Ruzhansky
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 141)

Abstract

In this paper we present LP and LP— Lq estimates for solutions of the Cauchy problem for some classes of pseudo-differential equations. First, we give estimates for operators with simple complex characteristic roots with non-negative imaginary parts. This class contains general strictly hyperbolic equations with variable coefficients. Then, we give sharp estimates for strictly hyperbolic differential operators with time dependent coefficients. The analysis is based on the corresponding LP and LP— Lq properties of Fourier integral operators with complex phase functions, which are also presented.

Keywords

Cauchy Problem Phase Function Hyperbolic Equation Fourier Integral Operator Lipschitz Space 
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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  1. 1.Department of Mathematics, Imperial CollegeUniversity of LondonLondonUnited Kingdom

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