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

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
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