On some differential invariants for a family of diffusion equations. (English) Zbl 1121.35006

Gandarias, M. L.; Torrisi, M.; Tracinà, R.

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 \(v_{t} = (v^{k}v_{x})_{x}\).

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