Homogenization for a non-local coupling model

authored by: R. Hochmuth
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.
External Organisation(s): University of Kassel
Type: Article
Journal: International Journal of Phytoremediation
Volume: 87
Pages: 1311-1323
No. of pages: 13
ISSN: 1522-6514
Publication date: 12.2008
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Environmental Chemistry, Pollution, Plant Science
Electronic version(s): https://doi.org/10.1080/00036810802555433 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{c86d911b0d624b288e3cef370f367c4a,
title = "Homogenization for a non-local coupling model",
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.",
keywords = "Bio-heat equation, Correctors, Heat transfer, Homogenization, Hyperthermia, Non-local boundary conditions, Robin boundary conditions",
author = "R. Hochmuth",
year = "2008",
month = dec,
doi = "10.1080/00036810802555433",
language = "English",
volume = "87",
pages = "1311--1323",
journal = "International Journal of Phytoremediation",
issn = "1522-6514",
publisher = "Taylor and Francis Ltd.",
number = "12",
}