Abstract
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 R^3 . 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 R^3 . 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 R^3 .
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