Phragmén-Lindelöf alternative results and structural stability for Brinkman fluid in porous media in a semi-infinite cylinder

Abstract

This article investigates the spatial behavior of the solutions of the Brinkman equations in a semi-infinite cylinder. We no longer require the solutions to satisfy any a priori assumptions at infinity. Using the energy estimation method and the differential inequality technology, the differential inequality about the solutions is derived. By solving this differential inequality, it is proved that the solutions grow polynomially or decay exponentially with spatial variables. In the case of decay, the structural stability of Brinkman fluid is also proved.