Transformation operators and their applications for modeling in two-layer media

We present a 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 at symmetry is obtained by the developed in this paper transformation operators method. Keywords: Poisson formula, Wave equation, Heat equation, Dirichlet problem, Laplace equation.