Poisson problems for semilinear Brinkman systems on Lipschitz domains in $${\mathbb{R}^n}$$ R n

Abstract

The purpose of this paper is to combine a layer potential analysis with the Schauder fixed point theorem to show the existence of solutions of the Poisson problem for a semilinear Brinkman system on bounded Lipschitz domains in $${{\mathbb R}^n (n\geq 2)}$$ with Dirichlet or Robin boundary conditions and data in L 2-based Sobolev spaces. We also obtain an existence and uniqueness result for the Dirichlet problem for a special semilinear elliptic system, called the Darcy–Forchheimer–Brinkman system.