Investigation of Two-dimensional Diffusion Equation with Random Dependence of the Diffusion Coefficient on Time

Student: Konyashina Valeriya

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Business Informatics (Bachelor)

Year of Graduation: 2016

Final qualification work is devoted to the study of the diffusion equation with random dependence of the diffusion coefficient on time. The proposal begins with the analysis of the general diffusion equation, then describes the output of the right equation’s form; secondly, the solution obtained is addressed, and finally the graph plotted depicts the result received. The exact equation has been found by converting a general diffusion equation by means of telegraphic process and the calculation of the correlation function and the right solution has been got in quadratures using modified Bessel functions and their properties. Moreover, the effect of anomalous diffusion has been examined. In future it seems worthwhile to update information and to put theory into practice.

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