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The Periodic Unfolding Method: Theory and Applications to Partial Differential Problems: 3 (Series in Contemporary Mathematics, 3) - Hardcover

Book 3 of 4: Series in Contemporary Mathematics

Cioranescu, Doina; Damlamian, Alain; Griso, Georges

 
9789811330315: The Periodic Unfolding Method: Theory and Applications to Partial Differential Problems: 3 (Series in Contemporary Mathematics, 3)
Hardcover
ISBN 10: 981133031X ISBN 13: 9789811330315
Publisher: Springer, 2018

Synopsis

This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems.

 Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV).  The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III).  A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V).  Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI).

This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

"synopsis" may belong to another edition of this title.

From the Back Cover

This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems.

 Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV).  The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III).  A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V).  Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI).

This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2018
Language
English
ISBN 10 
981133031X
ISBN 13 
9789811330315
Binding
Hardcover
Edition number
1
Number of pages
530