A nonlinear heat transfer equation in turbulent media: symmetry classification, recursion operators, and exact solutions

Abstract

We study a heat transfer equation in spatial dimensions $n = 1$, $2$, and $3$. A group classification with respect to the functional parameter $k = k(T)$ is done and symmetry algebras are presented. Recursion operators are found in the case $n = 1$ and infinite hierarchies of symmetries are constructed. We also find a number of exact solution in all the three cases.