We exploit a layer potential theoretic method and a fixed point theorem in order to show the existence of a solution of the Robin problem for a nonlinear system in a Lipschitz domain in ${\mathbb R}^n$ ($n\in \{2,3\}$) with a small boundary datum in $L^2$-based Sobolev spaces. Such a nonlinear system describes the flow of a viscous incompressible fluid in a saturated porous medium and is called the Darcy-Forchheimer-Brinkman system.
Nonlinear Darcy-Forchheimer-Brinkman system with linear Robin boundary conditions in Lipschitz domains
LANZA DE CRISTOFORIS, MASSIMO;
2014
Abstract
We exploit a layer potential theoretic method and a fixed point theorem in order to show the existence of a solution of the Robin problem for a nonlinear system in a Lipschitz domain in ${\mathbb R}^n$ ($n\in \{2,3\}$) with a small boundary datum in $L^2$-based Sobolev spaces. Such a nonlinear system describes the flow of a viscous incompressible fluid in a saturated porous medium and is called the Darcy-Forchheimer-Brinkman system.
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