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A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

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Abstract

In this paper the (2+1)-nonlinear diffusion equation u t −div(f(u)grad u)=0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.

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Authors and Affiliations

  1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Ashfaque H. Bokhari, Ahmad Y. Al Dweik & F. D. Zaman

  2. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

    A. H. Kara

Authors
  1. Ashfaque H. Bokhari
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  2. Ahmad Y. Al Dweik
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  3. A. H. Kara
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  4. F. D. Zaman
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Correspondence to A. H. Kara.

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Bokhari, A.H., Al Dweik, A.Y., Kara, A.H. et al. A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity. Nonlinear Dyn 62, 127–138 (2010). https://doi.org/10.1007/s11071-010-9704-8

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  • DOI: https://doi.org/10.1007/s11071-010-9704-8

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