Second-order differential invariants of a family of diffusion equations. (English) Zbl 1078.35051

Torrisi, M.; Tracinà, R.

J. Phys. A, Math. Gen. 38, No. 34, 7519-7526 (2005).

The nonlinear diffusion equation \(u_t-u_{xx}=f(u,u_x)\) is considered. By means of the Lie criterion of infinitesimal invariance the authors construct the Lie algebra \(L_{\varepsilon}\) of the equivalence transformations. Second order differential invariants with respect to the equivalence transformations of the equation are calculated. On this base the characterization of the subclass of nonlinear diffusion equations is given, which can be linearized through an equivalence transformation.

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC:

35K55	Nonlinear parabolic equations
76R50	Diffusion
70G65	Symmetries, Lie group and Lie algebra methods for problems in mechanics
58J70	Invariance and symmetry properties for PDEs on manifolds

Keywords:

Lie algebra of equivalence transformations; linearization possibilities