Classes of solutions for a nonlinear diffusion PDE (Q5946609)

The authors deal with the large time behavior of concentration -- a problem of interest in underground water pollution. By means of the asymptotic method and the method of separation of variables they reduce some 2D nonlinear second-order PDE, modelling underground water pollution to simpler ODEs. For them the authors obtain several classes of exact solutions, which are expressed in terms of various special functions. One of them has been used to compute momenta, and a perfect agreement with experimental data is found. This solution represents the first theoretical support to these data. It is very simple and similar to the corresponding solution from 1D case, which also provides a very good large time behaviour for the concentration of the pollutant.