On the smoothness properties of the solution of a nonlinear filtration problem in the presence of a point source

The properties of the solution of a nonlinear filtration problem in inhomogeneous porous media in the presence of a point source for a fluid obeying a law with a linear growth at infinity are studied. Additive selection of the feature connected with the singularity of the right-hand side is used. The pressure field is represented as the sum of the known solution of some linear (associated with the original) problem with a point source on the right-hand side and the unknown “additive term”. Hölder continuity of the second term is established.