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Title: Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems
Authors: Kohr, M
Lanza de Cristoforis, M
Mikhailov, S
Wendland, W
Keywords: The Stokes system;The Darcy-Forchheimer-Brinkman system;Transmission problems;Lipschitz domains in R3;Layer potentials;Weighted Sobolev spaces;Fixed point theorem
Issue Date: 2016
Citation: Zeitschrift fur angewandte Mathematik und Physik ZAMP, 67 (116), 2016
Abstract: The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces.
ISSN: 1420-9039
Appears in Collections:Dept of Mathematics Research Papers

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