On the smoothness of a solution of nonlinear filtration problem in the presence of a point source
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.
Keywords and phrasesnonlinear filtering heterogeneous medium point source Hölder continuity
Unable to display preview. Download preview PDF.
- 1.O. A. Zadvornov, “The existence of a solution for a quasilinear elliptic boundary value problem in the presence of point sources,” Uchen. Zap. Kazan. Univ. Ser. Fiz.-Mat. Nauki 125(1), 155–163 (2010).Google Scholar
- 3.M. M. Vainberg, Variational Methods for Studying Nonlinear Operators (Gostekhizdat, Moscow, 1956) [in Russian].Google Scholar