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Abstract and Applied Analysis
Volume 2015, Article ID 329052, 13 pages
http://dx.doi.org/10.1155/2015/329052
Research Article

Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium

1Department of Mathematical and Computing Modelling, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
2Faculty of Mathematics and Mechanics, L.N.Gumilyov Eurasian National University, Astana 010008, Kazakhstan

Received 23 May 2015; Revised 17 August 2015; Accepted 18 August 2015

Academic Editor: Sergei V. Pereverzyev

Copyright © 2015 Magira Kulbay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data.