eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2015-01-13 3 1 7 11 10.12691/ijpdea-3-1-2 IJPDEA2015312 article O. Yaremko yaremki@mail.ru 1 N. Yaremko 1 T. Eliseeva 1 Penza State University, str. Lermontov, 37, 440038, Penza, Russia 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. http://pubs.sciepub.com/ijpdea/3/1/2/ijpdea-3-1-2.pdf poisson formula wave equation heat equation dirichlet problem laplace equation