NONCLASSICAL SYMMETRY REDUCTIONS OF THE LINEAR DIFFUSION EQUATION WITH A NONLINEAR SOURCE

Nonclassical symmetry methods are used to study the linear diffusion e quation with a nonlinear source term. Mathematical forms are obtained for the source terms which permit a nonclassical symmetry reduction. I n addition to the known source terms obtainable from classical symmetr y methods, new source terms are found which also admit symmetry reduct ions. A number of examples are considered and several new exact soluti ons are constructed, some of which are illustrated graphically.