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Course, academic year 2024/2025
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An introduction to mathematical homogenization - NMMA469
Title: An introduction to mathematical homogenization
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: Stefan Krömer
Teacher(s): Stefan Krömer
Class: M Mgr. MA
M Mgr. MA > Volitelné
M Mgr. MOD
M Mgr. MOD > Volitelné
M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Differential Equations, Potential Theory, Mathematical Modeling in Physics
Annotation -
An introductory course of mathematical homogenization.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (07.09.2018)
Literature -

Cioranescu, Doina; Donato, Patrizia: An introduction to homogenization. Oxford Lecture Series in Mathematics and its Applications, 17. The Clarendon Press, Oxford University Press, New York, 1999.

Braides, Andrea; Defranceschi, Anneliese: Homogenization of multiple integrals. Oxford Lecture Series in Mathematics and its Applications, 12. The Clarendon Press, Oxford University Press, New York, 1998.

Last update: Krömer Stefan (26.08.2021)
Teaching methods

The course will be held in class. If the number of participants is very low, guided reading is a possible alternative.

For questions please contact me directly by email. Home page: http://www.utia.cas.cz/people/kr-mer

Last update: Krömer Stefan (13.09.2024)
Syllabus -

Basic periodic oscillations; Examples for periodic composites; Periodic homogenization for elliptic equations: formal expansions and correctors; Notions of convergence for homogenization problems: G-convergence, H-convergence, Gamma-convergence; Variational periodic homogenization for convex functionals, weak two-scale convergence

Last update: Kaplický Petr, doc. Mgr., Ph.D. (07.09.2018)
Entry requirements

Necessary prior knowledge: Functional analysis (weak topologies) and the Sobolev space W^{1,2}

Useful prior knowledge: Elliptic PDEs (weak formulation, existence, uniqueness), Calculus of Variations (direct methods)

Last update: Kaplický Petr, doc. Mgr., Ph.D. (07.09.2018)
 
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