Investigation of a nonlinear three-dimensional diffusion model of a porous medium
Yu. A. Chirkunov, Yu. L. Skolubovich · Journal of Physics Conference Series · 2019
We study a general three-dimensional nonlinear diffusion model of porous medium with non-stationary source or absorption. For the model, admitting the widest group Lie of the transformations we found some invariant solutions of rank 1. These include the following solutions: the generalizations of "a layered circular pie", "a layered plane pie", a generalization of "a layered spiral pie", "a layered conical pie", a solution with a radial distribution of the pressure, "a layered spherical pie". The obtained results can be used to study the processes associated with a underground fluid or gas flow, with water filtration, with the engineering surveys in the construction of the buildings, and also with shale oil and gas production.