Homogenization of the heat equation with a vanishing volumetric heat capacity
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Publication:1982760
DOI10.1007/978-3-030-27550-1_43zbMATH Open1469.80006arXiv1809.11019OpenAlexW2894398802MaRDI QIDQ1982760
T. Danielsson, Pernilla Johnsen
Publication date: 14 September 2021
Abstract: This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization result is established by using the evolution settings of multiscale and very weak multiscale convergence. In particular, we investigate how the relation between the volumetric heat capacity and the microscopic structure effects the homogenized problem and its associated local problem. It turns out that the properties of the microscopic geometry of the problem give rise to certain special effects in the homogenization result.
Full work available at URL: https://arxiv.org/abs/1809.11019
Optimization problems in thermodynamics and heat transfer (80M50) PDEs in connection with classical thermodynamics and heat transfer (35Q79)
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