Highfrequency asymptotic solution of the wave equation in an inhomogeneous medium

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Abstract

An explicit integral representation is obtained in the 0 limit of the solution of the wave equation utt=c(x)2u on Rn(n3) with initial data of the form u(x,0)=f(x)eiS(x)/. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by timedependent geometrical optics.

Original languageEnglish (US)
Pages (from-to)651-655
Number of pages5
JournalJournal of Mathematical Physics
Volume32
Issue number3
DOIs
StatePublished - Jan 1 1991
Externally publishedYes

Keywords

  • ASYMPTOTIC SOLUTIONS
  • FREQUENCY DEPENDENCE
  • GAUSS FUNCTION
  • GEOMETRICAL OPTICS
  • INHOMOGENEOUS MATERIALS
  • INTEGRALS
  • PULSES
  • QUANTUM MECHANICS
  • SEMICLASSICAL APPROXIMATION
  • TIME DEPENDENCE
  • WAVE EQUATIONS

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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