Classes of solutions for a nonlinear diffusion PDE

摘要

By means of asymptotic and separation of variables method some 2D nonlinear second-order PDE, modelling the underground water pollution, is reduced to simpler ODEs. For them several classes of exact solutions are deduced. They are expressed in terms of various special (e.g., hypergeometric, gamma, Bessel, Abel) functions. One of them was used to compute momenta. A perfect agreement with experimental data is found. This solution represents the first theoretical support for these data. It is very simple and is similar to the corresponding solution from the 1D case, which also provides a very good large time behavior for the concentration of the pollutant.