First-order compatibility for a (2 + 1)-dimensional diffusion equation

Abstract

A class of first-order partial differential equations is obtained compatible with a (2 + 1)-dimensional linear diffusion equation with a nonlinear source term. We will show that if the source term is quasilinear, then compatible equations are quasilinear. Furthermore, we obtain diffusion equations with source terms that admit non-quasilinear compatible equations.