On a preliminary group classification of the nonlinear heat conduction equation

Abstract

We apply the method of preliminary group classification to a particular form of the nonlinear heat equation,viz. u _t = f(u)u _xx + g(u)u _x ². This results in an optimal system of one-dimensional subalgebras required for the systematic reduction of partial differential equations (PDEs). This system of subalgebras yields different forms of f(u) and g(u) that allow for an additional symmetry. We also apply a preliminary group classification with respect to potential symmetries to a related system with g(u) = f′(u).