Revisiting the Group Classification of the General Nonlinear Heat Equation ut = (K(u)ux)x
Year: 2025
Type: article
Abstract: Group classification is a powerful tool for identifying and selecting the free elements—functions or parameters—in partial differential equations (PDEs) that maximize the symmetry properties of the model. In this paper, we revisit the group classification of the general nonlinear heat (or diffusion) equation ut=K(u)uxx, where K(u) is a non-constant function of the dependent variable. We present the group classification framework, derive the determining equations for the coefficients of the infinitesimal generators of the admitted symmetry groups, and systematically solve for admissible forms of K(u). Our analysis recovers the classical results of Ovsyannikov and Bluman and provides additional clarity and detailed derivations. The classification yields multiple cases, each corresponding to a specific form of K(u), and reveals the dimension of the associated Lie symmetry algebra.
Source: Mathematics
DOI: 10.3390/math13060911
Author: Winter Sinkala
Institution: Walter Sisulu University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408290688