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O. Yaremko, V. Selutin, N. Yaremko, The Fourier Transform with Piecewise Trigonometric Kernels and its Applications, WSEAS transactions on mathematics, Volume 13, 2014, pp. 615-625.

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Article

Vector Transformation Operators for a Systems Partial Differential Equation

1Penza State University, str. Lermontov, 37, 440038, Penza, Russia


International Journal of Partial Differential Equations and Applications. 2015, Vol. 3 No. 1, 7-11
DOI: 10.12691/ijpdea-3-1-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
O. Yaremko, N. Yaremko, T. Eliseeva. Vector Transformation Operators for a Systems Partial Differential Equation. International Journal of Partial Differential Equations and Applications. 2015; 3(1):7-11. doi: 10.12691/ijpdea-3-1-2.

Correspondence to: O.  Yaremko, Penza State University, str. Lermontov, 37, 440038, Penza, Russia. Email: yaremki@mail.ru

Abstract

Vector transformation operators method is applied to vector heat equation in one space dimension, to vector wave equation in one space dimension and to vector Laplace equation in two dimensions. The transformation operators method which allows us to interpret piecewise-homogeneous physical processes as a perturbing of a homogeneous ones. The analytical description of mathematical models of thermal conductivity and wave processes for piecewise homogeneous media with flat symmetry is obtained by the developed in this paper vector transformation operators method.

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