Abstract
Properties of a solution of a nonlinear filtration problem in a heterogeneous porous medium in the presence of a point source for a fluid obeying a linear growth law at infinity are studied. In the generalized setting of the problem, a singularity related to the singularity of the right-hand side is determined as an additive term. The pressure field is represented as the sum of a known solution of a certain linear problem (associated with the initial one) with a point source on the right-hand side and an unknown “addition.” The Hölder continuity of the latter term is proved.
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Original Russian Text © O.A. Zadvornov, G.O. Zadvornova, 2012, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Vol. 154, No. 1, pp. 162–166.
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Zadvornov, O.A., Zadvornova, G.O. On the smoothness of a solution of nonlinear filtration problem in the presence of a point source. Lobachevskii J Math 34, 412–415 (2013). https://doi.org/10.1134/S1995080213040070
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DOI: https://doi.org/10.1134/S1995080213040070