The purpose of this paper is to study boundary value problems of Robin type for the Brinkman system and a semilinear elliptic system, called the Darcy–Forchheimer–Brinkman system, on Lipschitz domains in Euclidean setting. In the first part of the paper, we exploit a layer potential analysis and a fixed point theorem to show the existence and uniqueness of the solution to the nonlinear Robin problem for the Darcy–Forchheimer–Brinkman system on a bounded Lipschitz domain in Rn (n ∈ {2, 3}) with small data in L2-based Sobolev spaces. In the second part, we show an existence result for the mixed Dirichlet–Robin problem for the same semilinear Darcy–Forchheimer-Brinkman system on a bounded creased Lipschitz domain in R3 with small L2-boundary data. We also study mixed Dirichlet–Robin problems and boundary value problems of mixed Dirichlet–Robin and transmission type for Brinkman systems on bounded creased Lipschitz domains in Rn (n ≥ 3). Finally, we show the well-posedness of the Navier problem for the Brinkman system with boundary data in some L2-based Sobolev spaces on a bounded Lipschitz domain in R3.

Boundary value problems of Robin type for the Brinkman and Darcy–Forchheimer–Brinkman systems in Lipschitz Domains

LANZA DE CRISTOFORIS, MASSIMO;
2014

Abstract

The purpose of this paper is to study boundary value problems of Robin type for the Brinkman system and a semilinear elliptic system, called the Darcy–Forchheimer–Brinkman system, on Lipschitz domains in Euclidean setting. In the first part of the paper, we exploit a layer potential analysis and a fixed point theorem to show the existence and uniqueness of the solution to the nonlinear Robin problem for the Darcy–Forchheimer–Brinkman system on a bounded Lipschitz domain in Rn (n ∈ {2, 3}) with small data in L2-based Sobolev spaces. In the second part, we show an existence result for the mixed Dirichlet–Robin problem for the same semilinear Darcy–Forchheimer-Brinkman system on a bounded creased Lipschitz domain in R3 with small L2-boundary data. We also study mixed Dirichlet–Robin problems and boundary value problems of mixed Dirichlet–Robin and transmission type for Brinkman systems on bounded creased Lipschitz domains in Rn (n ≥ 3). Finally, we show the well-posedness of the Navier problem for the Brinkman system with boundary data in some L2-based Sobolev spaces on a bounded Lipschitz domain in R3.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3038500
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