The equivalence transformation algebra $L_E$ and some of its differential invariants for the class of equations $u_t = (h(u)u_x)_x + f(x, u, u_x) (h ≠ 0)$ 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 $v_t = (v^kv_x)_x$.
On some differential invariants for a family of diffusion equations
TRACINA', RITA
2007-01-01
Abstract
The equivalence transformation algebra $L_E$ and some of its differential invariants for the class of equations $u_t = (h(u)u_x)_x + f(x, u, u_x) (h ≠ 0)$ 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 $v_t = (v^kv_x)_x$.File in questo prodotto:
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