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 Rn (n ≥ 2) with Dirichlet or Robin boundary conditions and data in L2-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.

Poisson problems for semilinear Brinkman systems on Lipschitz domains in Rn

LANZA DE CRISTOFORIS, MASSIMO;
2015

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 Rn (n ≥ 2) with Dirichlet or Robin boundary conditions and data in L2-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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3167713
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