The Nonlinear Diffusion Equation Describing Spread of Impurities of High Density

• Authors: A. Janavičius , G. Lūža , D. Jurgaitis
• Languages of publication: EN

Abstracts

EN

The nonlinear diffusion equation is derived by taking into account the local variations in the solvent density, within a mechanism of diffusion driven by random particle collisions. Analytical solutions for the case of spherical-symmetric nonlinear diffusion equation for spread of impurities in gas and solids are obtained and discussed. In this case, the solutions of the nonlinear diffusion equation are similar to solutions of Bernoulli equation. We note that the obtained solutions can be used to describe the shapes of impurity gas of high concentration or smoke clouds.

Keywords

EN

66.30.-h

Discipline

• 66.30.-h: Diffusion in solids(for surface and interface diffusion, see 68.35.Fx)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2004
• Volume: 105
• Issue: 5
• Pages: 475-483

Dates

published

2004-05

received

2004-05-06

Contributors

author

A. Janavičius

• Department of Physics and Mathematics, Šiauliai University, Višinskio 25, Šiauliai, 5400, Lithuania

author

G. Lūža

• Department of Physics and Mathematics, Šiauliai University, Višinskio 25, Šiauliai, 5400, Lithuania

author

D. Jurgaitis

• Department of Physics and Mathematics, Šiauliai University, Višinskio 25, Šiauliai, 5400, Lithuania

References

• 1. A.J. Janavičius, Random Processes and Transfer Phenomena, Šiauliai University, Šiauliai 2002, p. 85 (in Lithuanian)
• 2. A.J. Janavičius, Phys. Lett. A 224, 159 (1997)
• 3. B.-F. Apostol, Phys. Lett. A 235, 363 (1997)
• 4. P.F. Fil cakov, Handbook of High Mathematics, Naukova Dumka, Kiev 1973, p. 743 (in Russian)
• 5. G. Korn, T. Korn, Mathematical Handbook for Scientists and Engineers McGRAW-HILL Book Company, New York 1973, p. 684
• 6. M.E. Gliksman, Diffusion in Solids, John Wiley Sons, New York 2000, p. 472
• 7. W.-S. Wang, Y.-H. Lo, IEEE Trans. Electron Devices ED-30, 1828 (1983)
• 8. Laboratory Guide of Physics, Ed. L.L. Goldin, Nauka, Moscow 1983, p. 704 (in Russian)

Identifiers

DOI

10.12693/APhysPolA.105.475