Stationary processes of diffusion-convection-decomposition in a homogeneous half-space
UDC
539.3DOI:
https://doi.org/10.31429/vestnik-16-4-31-42Abstract
Algorithms for constructing the Fourier symbols of the Green's functions for stationary boundary problems of the 1st, 2nd, 3rd kind for a homogeneous diffusion half-space and an analogue of the second-kind problem for two linked half-spaces are developed, the properties of the symbols of fundamental solutions are investigated. Simple practical techniques are proposed for constructing a solution decreasing at infinity. For a boundary value problem of the third kind, it is shown that under certain boundary conditions the appearance of real and purely imaginary simple poles of the symbol of the Green's function is possible. Conditions were found under which these poles arise and conditions under which they are not guaranteed to arise. Three-dimensional model problems are calculated for all considered boundary value problems, which allow one to detect both similarities and differences of solutions. In the case of real poles, the solution differs significantly from all previous solutions. This solution is qualitatively similar to the patterns of anomalous diffusion in complex media.
Keywords:
stationary turbulent diffusion, boundary value problems, half-space, diffusion-convection-decay, Green's function, Fourier transformAcknowledgement
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Copyright (c) 2019 Syromyatnikov P.V., Krivosheeva M.A., Lapina O.N., Nesterenko A.G., Nikitin Yu.G.
This work is licensed under a Creative Commons Attribution 4.0 International License.
