Dj. Arrigo et al., NONCLASSICAL SYMMETRY REDUCTIONS OF THE LINEAR DIFFUSION EQUATION WITH A NONLINEAR SOURCE, IMA journal of applied mathematics, 52(1), 1994, pp. 1-24
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.