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The Cauchy Problem for Higher Order Equations

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

Abstract

A function of n real variables u(x1,..., xn) is said to be analytic in a domain D if for some neighborhood of each point P = (ξ1,...,ξn) in ·D it is representable as a multiple power series in the xi - ξi, i = 1,..., n,
$$ u({x_l}, \ldots ,{x_n}) = \sum\limits_{\mathop {{i_j} = l}\limits_{j = l,...,n} }^\infty {{a_{{i_l},...,{i_n}}}} {({x_i} - {\xi _i})^{{i_l}}} \ldots {({x_n} - {\xi _n})^{{i_n}}} $$
(1)
.

Keywords

Initial Data CAUCHY Problem Power Series Order Derivative Directional Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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