Journal of Mathematical Sciences

, Volume 218, Issue 6, pp 829–833 | Cite as

General Representation of Solutions of the Equation of Penetration and Diffusion of X-Rays in Plane Geometry

  • D. ShulaiaEmail author
  • P. Ghurtskaia


In this paper, we present a general procedure for solving of homogeneous equations that describe penetration and diffusion of X-rays in plane geometry. Starting from Van Kampen’s and Case’s observation that it suffices that “solutions” be distributions, elementary solutions of a homogeneous equation are found. We also prove that general solutions can be obtained by superposition of elementary solutions.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.I. Vekua Institute of Applied MathematicsTbilisiGeorgia
  2. 2.Georgian Technical UniversityTbilisiGeorgia

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