  A special class of symmetry reductions called nonclassical equivalence
transformations is discussed in connection to a class of parameter
identification problems represented by partial differential equations. These
symmetry reductions relate the forward and inverse problems, reduce the
dimension of the equation, yield special types of solutions, and may be
incorporated into the boundary conditions as well. As an example, we discuss
the nonlinear stationary heat conduction equation and show that this approach
permits the study of the model on new types of domains. Our MAPLE routine
GENDEFNC which uses the package DESOLV (authors Carminati and Vu) has been
updated for this propose and its output is the nonlinear partial differential
equation system of the determining equations of the nonclassical equivalence
transformations.
