Group Theoretic Similarity Solution of Second Order Nonlinear Diffusion Equation in an Isotropic Medium

Authors

  • K. J. Chauhan  Uttam Patel C. U. Shah Science College, Ashram Road, Ahmedabad, Gujarat, India

Keywords:

Diffusion Equations, Similarity Solutions, Infinitesimal Transformations

Abstract

In this paper the author discusses about the derivation of one-dimensional non-linear partial differential equation, which is associated with diffusion process. The infinitesimal transformations in searching for all possible groups of transformations to this partial differential equation are developed. The procedure is based on Lie’s theory of infinitesimal continuous group of transformations. This group theory has been applied extensively in recent times by investigators in the field of similarity analysis. By this method, this partial differential equation is reduced into the Abel’s equation of the second kind which is solved by the analytical method. The similarity solution is derived whenever the diffusivity coefficient varies linearly.

References

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International Journal of Scientific Research in Science, Engineering and Technology

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Published

2018-02-28

Issue

Volume 4, Issue 1, January-February-2018

Section

Research Articles

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How to Cite

[1]
K. J. Chauhan, " Group Theoretic Similarity Solution of Second Order Nonlinear Diffusion Equation in an Isotropic Medium, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 4, Issue 1, pp.1591-1594, January-February-2018.