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

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.