Homogenization for a Nonlocal Coupling Model

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 ac-count 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