Boundary integral approach for the mixed Dirichlet-Robin boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system

摘要

The purpose of this paper is to provide the solvability and uniqueness result to the mixed Dirichlet-Robin boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system in a bounded, two-dimensional Lipschitz domain. First we obtain a well-posedness result for the linear Brinkman system with Dirichlet-Neumann boundary conditions, by reducing the problem to the system of boundary integral equations based on the fundamental solution of the Brinkman system and by analyzing this system employing a variational approach. The result is extended afterwards to the Poisson problem for the Brinkman system and to Dirichlet-Robin boundary conditions, using the Newtonian potential and the linearity of the solution operator. Further, we study the nonlinear Darcy-Forchheimer-Brinkman boundary value problem of Dirichlet and Robin type. (C) 2019 Elsevier Ltd. All rights reserved.