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

• Fulltext

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

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

• Pramana – Journal of Physics

Volume 94, 2020
All articles
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• Editorial Note on Continuous Article Publication

Posted on July 25, 2019