Differential Invariants for Two and Three Dimensional Linear Parabolic Equations

Abstract

We find equivalence transformations for linear parabolic equations having two and three spatial dimensions. Invariants associated with these higher dimensional linear parabolic equations are derived using the obtained set of equivalence transformations. We apply Lie infinitesimal method to deduce the associated invariants. We find first order invariants for the the higher dimensional parabolic equations due to an invertible change of the dependent and independent variables separately. Further, obtained invariants are employed to reduce these linear higher dimensional parabolic equations to their simplest forms.