| Abstract: |
| Homogenization is a mathematical theory that takes a micro scale system and upscales it.
Applications of homogenization are multiple, e.g. in understanding biological tissue behavior, oil and gas extraction and geothermal energy systems. In 1989 Gabriel Nguetseng introduced in [1] the concept of two-scale convergence in the homogenization context. This has significantly simplified proofs and has, therefore, facilitated the applicability of the theory. In 2003 and 2004 he generalized this concept in [2, 3] even further with the notion of a homogenization structure. He showed that two-scale convergence is intimately linked with the mathematical description of the structure of the microscopic domain (such as porous rock). Currently his theory has only been applied to deterministic and static stochastic systems. In this talk we provide further developments concerning the homogenization of a PDE system connected to sulfate corrosion of concrete.\
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This represents joint work with Adrian Muntean (Karlstad, Sweden)
[1] G. Nguetseng, 1989, \textit{A General Convergence Result for a Functional Related to the Theory of Homogenization},SIAM J. Math. Anal. 20 (3), 608-623
[2] G. Nguetseng, 2003, \textit{Homogenization Structures and Applications I}, Z. Anal. Anwend. 22 (1), 73-107
[3] G. Nguetseng, 2004, \textit{Homogenization Structures and Applications I}, Z. Anal. Anwend. 23 (3), 483-508 |
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