Inverse Zommerfeld´s problem for fractal media

Author

Bondarenko, Anatoly N. ; Ivaschenko, Dmitry S. ; Seleznev, Vadim A.

Author_Institution

Inst. of Math., Novosibirsk, Russia

fYear

2002

fDate

2002

Firstpage

246

Lastpage

252

Abstract

The generalized Zommerfeld problem for fractal media was investigated. The Nigmatullin model describing the anomalous diffusion processes was considered as the model of the medium. The inverse problem, consisting in obtaining the heat conductivity coefficient and the anomalous diffusion exponent, by taking the temperature at the boundary points, is discussed. Having obtained the anomalous diffusion exponent one gets to restore the type of a differential equation. The numerical results illustrate some sudden properties of the point heat source influence function and correlations supplementing the well-known Fourier laws in the case of fractional medium are presented.

Keywords

Laplace transforms; boundary-value problems; diffusion; fractals; heat conduction; inverse problems; partial differential equations; Fourier laws; Laplace transform; Riemann-Liouville fractional derivative; anomalous diffusion processes; boundary points temperature; convolution; differential equation; diffusive wave; fractal media; fractional differentiation operator; generalized Zommerfeld´s problem; heat conductivity coefficient; inverse problems; point heat source influence function; semi-infinite rod; Bonding; Conductivity; Differential equations; Diffusion processes; Fractals; Fractional calculus; Inverse problems; Mathematics; Microscopy; Temperature;

fLanguage

English

Publisher

ieee

Conference_Titel

Science and Technology, 2002. KORUS-2002. Proceedings. The 6th Russian-Korean International Symposium on

Print_ISBN

0-7803-7427-4

Type

conf

DOI

10.1109/KORUS.2002.1028011

Filename

1028011