Lambert function and exact solutions of nonlinear parabolic equations

We consider the diffusion equations with degree type coefficient of diffusion and a nonlinear source. The main attention is paid to the construction of exact solutions expressed via the Lambert function. We prove a series of statements that determine the conditions for the source function that guarantee the existence of exact solutions of a certain type. We give examples of exact solutions of nonlinear diffusion equations (including those equations with polynomial and fractional-rational source functions) to illustrate the obtained results.