Asymptotic solutions and spectral theory of linear wave equations

Details Asymptotic solutions and spectral theory of linear wave equations Asymptotic solutions and spectral theory of linear wave equations

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phr....86..217a&link_type=abstract

Physics Reports, Volume 86, Issue 5, p. 217-316.

Physics

13

Scientific paper

This review contains two closely related strands. Firstly the Asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method [4] for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation-particularly spectral theory-are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of Astrophysical (particularly solar) and geophysical fluid dynamimics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interested in problems of linear wave propagation in these areas.

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