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
• Teaching methods: full-time
• Guarantor: 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

English

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

An introductory course of mathematical homogenization.

Czech

Last update: doc. RNDr. Pavel Pyrih, CSc. (14.05.2019)

Uvodni kurz matematicke homogenizace.

Literature

English

Last update: Stefan Krömer (26.08.2021)

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.

Teaching methods

Last update: Stefan Krömer (26.08.2021)

As long as it is possible, the course will be held in person. If necessary, further information will be added here later.

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

Syllabus

English

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

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

Czech

Last update: doc. RNDr. Pavel Pyrih, CSc. (14.05.2020)

Budou probírány základy matematicke homogenizace:

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

Entry requirements

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

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)