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IMA Journal of Applied Mathematics Advance Access originally published online on November 17, 2007
IMA Journal of Applied Mathematics 2008 73(2):374-392; doi:10.1093/imamat/hxm023
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Mirela Kohr{dagger}

Faculty of Mathematics and Computer Science, Babe-Bolyai University, 1 M. Kogalniceanu Street, 400084 Cluj-Napoca, Romania

G. P. Raja Sekhar{ddagger}

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India

John R. Blake§

School of Mathematics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

{dagger} Email: mkohr{at}math.ubbcluj.ro

{ddagger} Email: rajas{at}maths.iitkgp.ernet.in

§ Email: J.R.Blake{at}bham.ac.uk

Received on October 6, 2006; Accepted on May 23, 2007

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

Keywords: anisotropic case; Brinkman's equation; Fourier transform method; Green's function.


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