Homogenization of Partial Differential Equations using Multiscale Convergence Methods
The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of...
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| Format: | Others |
| Language: | English |
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Mittuniversitetet, Institutionen för matematik och ämnesdidaktik
2021
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| Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-42036 http://nbn-resolving.de/urn:isbn:978-91-89341-11-1 |
| Summary: | The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type. |
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