Homogenization of Differential Operators and Integral Functionals:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathematical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of nonlinear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogenization problems for partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each separate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the constituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc |
| Physical Description: | 1 Online-Ressource (XI, 570 p) |
| ISBN: | 9783642846595 9783642846618 |
| DOI: | 10.1007/978-3-642-84659-5 |
Staff View
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Record in the Search Index
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| author | Žikov, Vasilij Vasil'evič 1940-2017 |
| author_GND | (DE-588)106795063X (DE-588)114199051 |
| author_facet | Žikov, Vasilij Vasil'evič 1940-2017 |
| author_role | aut |
| author_sort | Žikov, Vasilij Vasil'evič 1940-2017 |
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| building | Verbundindex |
| bvnumber | BV042423044 |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-84659-5 |
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| id | DE-604.BV042423044 |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642846595 9783642846618 |
| language | English |
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| spelling | Žikov, Vasilij Vasil'evič 1940-2017 Verfasser (DE-588)106795063X aut Homogenization of Differential Operators and Integral Functionals by V. V. Jikov, S. M. Kozlov, O. A. Oleinik Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (XI, 570 p) txt rdacontent c rdamedia cr rdacarrier It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathematical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of nonlinear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogenization problems for partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each separate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the constituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Homogenisieren (DE-588)4138007-1 gnd rswk-swf Homogenisierungsmethode (DE-588)4257770-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Homogenisieren (DE-588)4138007-1 s 1\p DE-604 Homogenisierungsmethode (DE-588)4257770-6 s 2\p DE-604 Kozlov, S. M. Sonstige oth Olejnik, Olʹga A. 1925-2001 Sonstige (DE-588)114199051 oth https://doi.org/10.1007/978-3-642-84659-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Žikov, Vasilij Vasil'evič 1940-2017 Homogenization of Differential Operators and Integral Functionals Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisieren (DE-588)4138007-1 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4138007-1 (DE-588)4257770-6 |
| title | Homogenization of Differential Operators and Integral Functionals |
| title_auth | Homogenization of Differential Operators and Integral Functionals |
| title_exact_search | Homogenization of Differential Operators and Integral Functionals |
| title_full | Homogenization of Differential Operators and Integral Functionals by V. V. Jikov, S. M. Kozlov, O. A. Oleinik |
| title_fullStr | Homogenization of Differential Operators and Integral Functionals by V. V. Jikov, S. M. Kozlov, O. A. Oleinik |
| title_full_unstemmed | Homogenization of Differential Operators and Integral Functionals by V. V. Jikov, S. M. Kozlov, O. A. Oleinik |
| title_short | Homogenization of Differential Operators and Integral Functionals |
| title_sort | homogenization of differential operators and integral functionals |
| topic | Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisieren (DE-588)4138007-1 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Distribution (Probability theory) Analysis Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Mathematik Partielle Differentialgleichung Homogenisieren Homogenisierungsmethode |
| url | https://doi.org/10.1007/978-3-642-84659-5 |
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