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Homogenization for a Nonlocal Coupling Model

Please always quote using this URN: urn:nbn:de:0297-zib-8251
  • In [7,8,12] 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 nonlocal boundary conditions on parts of the boundary. Moreover, we present asymptotic estimates for first order correctors.

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Metadaten
Author:Reinhard Hochmuth
Document Type:ZIB-Report
Tag:Homogenization; Robin boundary conditions; bio-heat equation; correctos; heat transfer; hyperthermia; nonlocal boundary conditions
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B27 Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J25 Boundary value problems for second-order elliptic equations
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A20 Heat and mass transfer, heat flow
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Date of first Publication:2004/12/20
Series (Serial Number):ZIB-Report (04-50)
ZIB-Reportnumber:04-50
Published in:Appeared in: Appl. Anal. 87, No.12, 1311-1323 (2008)
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