On the invariants of two dimensional linear parabolic equations

We consider the most general two dimensional linear parabolic equations. Motivated by the recent work of Ibragimov et al. [1–3] we construct differential invariants, semi-invariants and invariant equations. These results are achieved with the employment of the equivalence group admitted by this class of parabolic equations. We derive those variable coefficient equations of this class of linear parabolic equations that can be mapped into constant coefficient equations. Further applications are presented.