@article {Hochmuth:December 2008:0003-6811:1311,
	author = "Hochmuth, R.",
	title = "Homogenization for a non-local coupling model",
	journal = "Applicable Analysis",
	volume = "87",
	year = "December 2008",
	abstract = "In [P. Deuflhard and R. Hochmuth, On the thermoregulation in the human microvascular system, Proc. Appl. Math. Mech. 3 (2003), pp. 378-379; P. Deuflhard and R. Hochmuth, Multiscale analysis of thermoregulation in the human microsvascular system, Math. Meth. Appl. Sci. 27 (2004), pp. 971-989; R. Hochmuth and P. Deuflhard, Multiscale analysis for the bio-heat transfer equation-the nonisolated case, Math. Models Methods Appl. Sci. 14(11) (2004), pp. 1621-1634], homogenization techniques are applied to derive an anisotropic variant of the bio-heat transfer equation as asymptotic result of boundary value problems providing a microscopic description for microvascular tissue. In view of a future application on treatment planning in hyperthermia, we investigate here the homogenization limit for a coupling model, which takes additionally into account the influence of convective heat transfer in medium-size blood vessels. This leads to second-order elliptic boundary value problems with non-local boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first-order correctors.",
	pages = "1311-1323(13)",
	url = "http://www.ingentaconnect.com/content/tandf/gapa/2008/00000087/00000012/art00003"
	doi = "doi:10.1080/00036810802555433"
}