Green's function of the Brinkman equation in a 2D anisotropic case

The purpose of this paper is to obtain the Green's functionof the Brinkman equation in a 2D case of hydrodynamic anisotropywith respect to the permeability. The anisotropic nature ofthe permeability is assumed to be not space or time dependent.We use the method of Fourier transform which reduces the computationof the Green's function to the computation of the fundamentalsolution of a fourth-order partial differential equation. Thisresearch work has several applications in engineering and medicineto the motion of bodies in anisotropic porous media.