Authors : Oleg Anatolyevich Zadvornov and Galina Olegovna Trifonova
Abstract: This study discusses a nonuniform stationary nonlinear filtering problem with degeneration at the presence of a point source. The filtration law has a linear growth at infinity and is monotonous one. The pressure is considered to be known at the boundary. The solution to this problem exists and has an additive representation with an explicit peculiarity in one summand, generated by the presence of a concentrated source. A variation problem is formulated for a second term and the method of simple iteration is applied. The filtration area proves the convergence of the iteration process at a geometric rate in the uniform norm and the value of an optimal parameter is obtained. Then, we prove the Holder continuity of the second summand within the field of filtration.
Oleg Anatolyevich Zadvornov and Galina Olegovna Trifonova, 2015. Heterogeneous Stationary Nonlinear Filtration Problem with Degeneration If a Point Source is Available. Research Journal of Applied Sciences, 10: 391-396.