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JOURNALS // Contemporary Mathematics and Its Applications // Archive

Contemporary Mathematics and Its Applications, 2015 Volume 97, Pages 133–137 (Mi cma431)

General representation of solutions of the equation of penetration and diffusion of X-rays in plane geometry

D. Shulaiaa, P. Ghurtskaiab

a Tbilisi Ivane Javakhishvili State University, Ilia Vekua Institute of Applied Mathematics
b Georgian Technical University

Abstract: 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.

UDC: 517.958

Language: English


 English version:
Journal of Mathematical Sciences, 2016, 218:6, 829–833


© Steklov Math. Inst. of RAS, 2024