Titlebook: Getting Acquainted with Homogenization and Multiscale; Leonid Berlyand,Volodymyr Rybalko Textbook 2018 Springer Nature Switzerland AG 2018

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Conscientious

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An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads, typically the most challenging part in the .-convergence approach, we use the convex duality approach. This parallels with the study of linear conductivity problem from . which also uses the idea of convex duality.

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https://doi.org/10.1007/978-3-662-67828-2ne and two. This Chapter contains also an example of an inverse homogenization problem for thermo-elasticity. We describe mathematical features of this problem in a 1D setting and discuss the effect of negative effective thermal expansion observed in 2D and 3D cases, which is rather counterintuitive.

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What Is Homogenization and Multiscale? First Examples,ne and two. This Chapter contains also an example of an inverse homogenization problem for thermo-elasticity. We describe mathematical features of this problem in a 1D setting and discuss the effect of negative effective thermal expansion observed in 2D and 3D cases, which is rather counterintuitive.

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Introduction to Stochastic Homogenization,cloud. These examples are easy on the intuitive level but their rigorous mathematical understanding requires significant effort for someone with no experience in stochastic modeling. We conclude the chapter by a brief discussion of recent developments and provide a number of references for further reading.

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,Kompaktheit und Abbildungsr?ume,s and facts about functional spaces are presented in more detail, especially those concerning Sobolev spaces. Special attention is also paid to the notion of weak convergence which plays a key role in homogenization theory. Since the book deals with PDEs, the chapter contains a minimal background on