LEADER 03958nam 22006255 450 001 9910300116703321 005 20200703131434.0 010 $a3-030-01777-X 024 7 $a10.1007/978-3-030-01777-4 035 $a(CKB)4100000007158903 035 $a(DE-He213)978-3-030-01777-4 035 $a(MiAaPQ)EBC6312528 035 $a(PPN)232472173 035 $a(EXLCZ)994100000007158903 100 $a20181122d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGetting Acquainted with Homogenization and Multiscale /$fby Leonid Berlyand, Volodymyr Rybalko 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (XVIII, 178 p. 42 illus., 14 illus. in color.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 311 $a3-030-01776-1 320 $aIncludes bibliographical references and index. 327 $aChapter 1- Preliminaries -- Chapter 2- What is Homogenization and Multiscale? First Examples -- Chapter 3- Brief History and Surprising Examples in Homogenization -- Chapter 4- Formal Two-scale Asymptotic Expansions and the Corrector Problem -- Chapter 5- Compensated Compactness and Oscillating Test-functions -- Chapter 6- Two-scale Convergence -- Chapter 7- Examples of Explicit Effective Coefficients: Laminated Structures and 2D Checkerboards -- Chapter 8- Introduction to Stochastic Homogenization -- Chapter 9- G-Convergence in Nonlinear Homogenization Problems -- Chapter 10- An Example of a Nonlinear Problem: Homogenization of Plasticity and Limit Loads -- Chapter 11- Continuum Limits for Discrete Problems with Fine Scales -- References -- Appendix: Regular and Singular Perturbations and Boundary Layers -- Index. 330 $aThe objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students. 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aComputer mathematics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aPartial differential equations 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aComputer mathematics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aPartial differential equations. 615 14$aComputational Science and Engineering. 615 24$aMathematical and Computational Engineering. 615 24$aPartial Differential Equations. 676 $a515.353 676 $a515.35 700 $aBerlyand$b Leonid$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768261 702 $aRybalko$b Volodymyr$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300116703321 996 $aGetting Acquainted with Homogenization and Multiscale$92266035 997 $aUNINA