A non-linear and non-local boundary condition for a diffusion equation in petroleum engineering

被引：4

作者：

Giroire, J ^{[1
]}

Ha-Duong, T ^{[1
]}

Moumas, V ^{[1
]}

机构：

[1] Univ Technol Compiegne, Ctr Rech Royallieu, Lab Math Appl Compiegne, F-60205 Compiegne, France

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2005年 / 28卷 / 13期

关键词：

petroleum flow; non-linear boundary condition; fixed point theorems;

D O I：

10.1002/mma.622

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals with a boundary value problem for Laplace equation with a non-linear and non-local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non-linear and non-local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright (c) 2005 John Wiley & Sons, Ltd.

引用

页码：1527 / 1552

页数：26

共 50 条

[1] Non-linear Schrodinger equation with non-local regional diffusion
Felmer, Patricio
Torres, Cesar
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) : 75 - 98
[2] Non-linear Schrödinger equation with non-local regional diffusion
Patricio Felmer
César Torres
[J]. Calculus of Variations and Partial Differential Equations, 2015, 54 : 75 - 98
[3] On the decomposition method to the heat equation with non-linear and non-local boundary conditions
Hadizadeh, M
Maleknejad, K
[J]. KYBERNETES, 1998, 27 (4-5) : 426 - +
[4] A PERIODICAL SOLUTION TO DIFFUSION EQUATION WITH A NON-LINEAR BOUNDARY CONDITION
KOCHINA, NN
[J]. DOKLADY AKADEMII NAUK SSSR, 1968, 179 (06): : 1297 - &
[5] Existence and multiplicity of solutions for a non-linear Schrodinger equation with non-local regional diffusion
Alves, Claudianor O.
Torres Ledesma, Cesar E.
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (11)
[6] NON-LOCAL PROBLEM WITH NON-LINEAR CONDITIONS FOR A HYPERBOLIC EQUATION
Dmitriev, V. B.
[J]. VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2009, (01): : 26 - 32
[7] From Becker-Doring to Lifshitz-Slyozov: deriving the non-local boundary condition of a non-linear transport equation
Yvinec, Romain
Deschamps, Julien
Hingant, Erwan
[J]. WORKSHOP ON MULTISCALE AND HYBRID MODELLING IN CELL AND CELL POPULATION BIOLOGY, 2015, 5
[8] Dynamics of electrorheological clutch and a problem for non-linear parabolic equation with non-local boundary conditions
Litvinov, W. G.
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 2008, 73 (04) : 619 - 640
[9] Symmetric ground state solution for a non-linear Schrodinger equation with non-local regional diffusion
Torres Ledesma, Cesar E.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (10) : 1375 - 1388
[10] Dynamics of electrorheological clutch and a problem for non-linear parabolic equation with non-local boundary conditions
Litvinov, W.G.
[J]. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 2008, 73 (04): : 619 - 640

← 1 2 3 4 5 →