Symmetry analysis of the two-dimensional diffusion equation with a source term (Q886164)

The authors study the two-dimensional diffusion equation \(u_t=u_{xx}+u_{yy}+Q(u,u_x,u_y)\) where it is assumed that the source \(Q\) effectively depends on both derivatives. The main part of the paper consists of a lengthy calculation in which several classes of sources admitting non-trivial Lie point symmetries are identified (no complete classification is given). Then the authors proceed to non-classical symmetries, however only in the restricted form of Bluman-Cole. They show that this extension does not lead to different results in the considered cases.