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Homogenization theory is a powerful method for modeling the microstructure of composite materials, including superconductors and optical fibers. This book is a complete introduction to the theory. It includes background material on partial differential equations and chapters devoted to the steady and non-steady heat equations, the wave equation, and the linearized system of elasticity.

Homogenization (Differential equations) --- Materials --- Homogénéisation (Equations différentielles) --- Matériaux --- Mathematical models. --- Modèles mathématiques --- 517.95 --- 519.63 --- 681.3*G18 --- Partial differential equations --- Numerical methods for solution of partial differential equations --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Homogenization (Differential equations). --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- 517.95 Partial differential equations --- Homogénéisation (Equations différentielles) --- Matériaux --- Modèles mathématiques --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Differential equations, Partial --- Mathematical models --- 681.3 *G18

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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.

Homogenization (Differential equations) --- Differential equations, Partial --- Differential equations, partial. --- Mechanics, applied. --- Partial Differential Equations. --- Theoretical and Applied Mechanics. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Partial differential equations

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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.

Partial differential equations --- Differential equations --- Classical mechanics. Field theory --- Applied physical engineering --- differentiaalvergelijkingen --- toegepaste mechanica --- mechanica