• An analysis of the nonlinear equation $u_t = f(x, u)u_{xx} + g(x, u)u^2_x + h(x, u)u_x + p(x, u)$

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/076/01/0023-0036

    • Keywords

       

      Partial differential equations; symmetries, nonlinear diffusion equation.

    • Abstract

       

      We use the method of preliminary group classification to analyse a particular form of the nonlinear diffusion equation in which the inhomogeneity is quadratic in $u_x$. The method yields an optimal system of one-dimensional subalgebras. As a result we obtain those explicit forms of the unknown functions 𝑓, 𝑔, ℎ and 𝑝 for which the equation admits additional point symmetries.

    • Author Affiliations

       

      R M Edelstein1 K S Govinder1

      1. Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu–Natal, Private Bag X54001, Durban 4000, South Africa
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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