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The Cauchy Problem for Linear Hyperbolic Equations in General

Part of the Applied Mathematical Sciences book series (AMS, volume 1)

Abstract

We begin with the second order linear equation in two independent variables
$$a{u_{xx}}\; + \;2b{u_{xy}}\; + \;c{u_{yy}}\; + \;d{u_x}\; + \;e{u_y}\; + \;f\; = \;g,\;$$
(1)
where the coefficients a,b,c,... are given functions of x and y in a domain D, having continuous second derivatives in D and satisfying the condition for being hyperbolic, ac — b2 < 0.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • F. John
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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