Analysis of stationary filtration problems with a multivalued law in the presence of several point sources

被引：0
作者：
Badriev, I. B. [1 ]
Zadvornov, O. A. [1 ]
机构：
[1] Kazan VI Lenin State Univ, Kazan 420008, Russia
来源：
DIFFERENTIAL EQUATIONS | 2008年 / 44卷 / 07期
基金：
俄罗斯基础研究基金会;
关键词：
Point Source; Variational Inequality; Dirichlet Problem; Iteration Method; Multivalued Function;
D O I：
10.1134/S0012266108070082
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We suggest a generalized statement of stationary filtration problems for an incompressible fluid obeying a multivalued filtration law with limit gradient in an arbitrary bounded nonone-dimensional domain in the presence of several point sources modeled by delta functions. The function determining the filtration law is assumed to grow linearly at infinity. The problems are stated in the form of an integral variational inequality of the second kind. We prove existence theorems and study the properties of solutions. To solve the problem, we suggest an iteration method whose each step essentially amounts to solving the Dirichlet problem for the Poisson equation.
引用
收藏
页码：960 / 969
页数：10
相关论文
共 13 条
  • [1] ALISHAEV MG, 1968, TEORIYA PRAKTIKA DOB, P202
  • [2] [Anonymous], 1974, TEORIYA EKSTREMALNYK
  • [3] BADRIEV IB, 2005, DIFF URAVN, V41, P874
  • [4] BADRIEV IB, 2007, DIFF URAVN, V43, P905
  • [5] BADRIEV IB, 2003, DIFF URAVN, V39, P888
  • [6] Ekeland I., 1976, Convex Analysis and Variational Problems
  • [7] ENTOV VM, 1989, MATEMATICHESKAYA TEO
  • [8] KARCHEVSKII MM, 1979, CHISLENNYE METODY ME, V10, P63
  • [9] Lapin A. V., 1979, Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, V19, P689
  • [10] Lions JL., 1969, Quelques methodes de resolution des problemes aux limites non lineaires
12