Homogenization for a non-local coupling model
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In: Applicable analysis. An international journal, Vol. 87, No. 12, 01.12.2008, p. 1311-1323.
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - Homogenization for a non-local coupling model
AU - Hochmuth, Reinhard
PY - 2008/12/1
Y1 - 2008/12/1
N2 - 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.
AB - 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.
KW - Mathematics
KW - homogenization
KW - non-local boundary conditions
KW - Robin boundary
KW - conditions
KW - correctors
KW - heat transfer
KW - bio-heat equation
KW - hyperthermia
UR - http://www.scopus.com/inward/record.url?scp=85064779521&partnerID=8YFLogxK
U2 - 10.1080/00036810802555433
DO - 10.1080/00036810802555433
M3 - Journal articles
VL - 87
SP - 1311
EP - 1323
JO - Applicable analysis. An international journal
JF - Applicable analysis. An international journal
SN - 0003-6811
IS - 12
ER -