Fundamental Transformations to Inhomogeneous Parabolic PDEs

The present paper is devoted to inhomogeneous (1 + 1) parabolic equations. In particular, we find a mapping which transforms the equations into a target equation. We prove a necessary condition which allows for the inhomogeneity to vanish. Consequently, we provide a concise presentation on a method of integrability of these equations. The theory is illustrated by several examples.