Gandarias, M. L.; Torrisi, M.; Tracinà, R. On some differential invariants for a family of diffusion equations. (English) Zbl 1121.35006 J. Phys. A, Math. Theor. 40, No. 30, 8803-8813 (2007). Summary: The equivalence transformation algebra \(L_{E}\) and some of its differential invariants for the class of equations \(u_{t} = (h(u)u_{x})_{x} + f(x, u, u_{x}) (h \neq 0)\) are obtained. Using these invariants, we characterize subclasses which can be mapped by means of an equivalence transformation into the well-studied family of equations \(v_{t} = (v^{k}v_{x})_{x}\). Cited in 12 Documents MSC: 35A30 Geometric theory, characteristics, transformations in context of PDEs 35K57 Reaction-diffusion equations 58J70 Invariance and symmetry properties for PDEs on manifolds Keywords:transformation algebra; equivalence transformation PDF BibTeX XML Cite \textit{M. L. Gandarias} et al., J. Phys. A, Math. Theor. 40, No. 30, 8803--8813 (2007; Zbl 1121.35006) Full Text: DOI OpenURL