Geodesic
On the smoothness properties of the solution of a nonlinear filtration problem in the presence of a point source
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 162-166

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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.
Keywords: nonlinear filtration, inhomogeneous medium
Mots-clés : point source, Hölder continuity. 
@article{UZKU_2012_154_1_a13,
     author = {O. A. Zadvornov and G. O. Zadvornova},
     title = {On the smoothness properties of the solution of a~nonlinear filtration problem in the presence of a~point source},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {162--166},
     publisher = {mathdoc},
     volume = {154},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a13/}
}
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O. A. Zadvornov; G. O. Zadvornova. On the smoothness properties of the solution of a nonlinear filtration problem in the presence of a point source. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 162-166. http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a13/