@misc{Hochmuth, author = {Hochmuth, Reinhard}, title = {Homogenization for a Nonlocal Coupling Model}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8251}, number = {04-50}, abstract = {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.}, language = {en} } @misc{HochmuthDeuflhard, author = {Hochmuth, Reinhard and Deuflhard, Peter}, title = {Multiscale Analysis for the Bio-Heat Transfer Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7302}, number = {03-08}, abstract = {The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In [{\sl Deuflhard, Hochmuth 2002}] the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected. Moreover, asymptotic corrector results are derived.}, language = {en} }