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Authors: ANDREI-FLORIN ALBIŞORU.
The purpose of this paper is to treat a nonlinear transmission-type problem for a generalized version of the Darcy-Forchheimer-Brinkman system and the classical Brinkman system in complementary Lipschitz domains in R3.
First of all, we define the required spaces in which we seek our solution. Next, we describe the generalized Brinkman and the generalized Darcy-Forchheimer-Brinkman systems. Further, we give important lemmas that allow us to introduce the trace and conormal derivative operators that appear in the formulation of our transmission problem. We invoke a result regarding the well-posedness of the (linear) transmission problem for the generalized and classical Brinkman systems in complementary Lipschitz domains in R3. The above mentioned well-posedness result in the linear case combined with Banach''s fixed point theorem will allow us to establish the main result of the paper, the well-posedness of the transmission problem for the Brinkman system and the nonlinear generalized Darcy-Forchheimer-Brinkman system in Lipschitz domains in R3.
Mathematics Subject Classification (2010): 35J25, 35Q35, 46E35.
Keywords: Sobolev spaces, generalized Brinkman system, transmission problems, generalized Darcy-Forchheimer-Brinkman system, well-posedness result, Banach fixed point theorem.
