47
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Homogenization for a non-local coupling model

Pages 1311-1323 | Received 23 Nov 2007, Accepted 13 Oct 2008, Published online: 21 Sep 2010
 

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.

Mathematics Subject Classifications: :

Acknowledgement

The author has been supported by a Konrad-Zuse-Fellowship. In particular, he is grateful to Peter Deuflhard for stimulating and valuable comments during the preparation of this article.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.