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Gamma-convergence for Beginners

Author: Andrea Braides

Publisher: Clarendon Press

Published: 2002

Total Pages: 231

ISBN-13: 0198507844

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The point of the technique is to describe the asymptotic behavior of families of minimum problems. This textbook was developed from a lectures series for doctoral students in applied functional analysis to describe all the main features of the convergence to an audience primarily interested in applications but not intending to enter the specialty. Annotation copyrighted by Book News, Inc., Portland, OR

Book Synopsis Gamma-convergence for Beginners by : Andrea Braides

Download or read book Gamma-convergence for Beginners written by Andrea Braides and published by Clarendon Press. This book was released on 2002 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The point of the technique is to describe the asymptotic behavior of families of minimum problems. This textbook was developed from a lectures series for doctoral students in applied functional analysis to describe all the main features of the convergence to an audience primarily interested in applications but not intending to enter the specialty. Annotation copyrighted by Book News, Inc., Portland, OR

An Introduction to Γ-Convergence

Author: Gianni Dal Maso

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 351

ISBN-13: 1461203279

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Book Synopsis An Introduction to Γ-Convergence by : Gianni Dal Maso

Download or read book An Introduction to Γ-Convergence written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gamma-convergence for Beginners

Author: Andrea Braides

Publisher: Clarendon Press

Published: 2002

Total Pages: 238

ISBN-13: 9780198507840

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Book Synopsis Gamma-convergence for Beginners by : Andrea Braides

Download or read book Gamma-convergence for Beginners written by Andrea Braides and published by Clarendon Press. This book was released on 2002 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The point of the technique is to describe the asymptotic behavior of families of minimum problems. This textbook was developed from a lectures series for doctoral students in applied functional analysis to describe all the main features of the convergence to an audience primarily interested in applications but not intending to enter the specialty. Annotation copyrighted by Book News, Inc., Portland, OR

An Introduction to [gamma]-convergence

Author: Gianni Dal Maso

Publisher:

Published: 1993-01-01

Total Pages: 340

ISBN-13: 9783764336790

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Book Synopsis An Introduction to [gamma]-convergence by : Gianni Dal Maso

Download or read book An Introduction to [gamma]-convergence written by Gianni Dal Maso and published by . This book was released on 1993-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Local Minimization, Variational Evolution and Γ-Convergence

Author: Andrea Braides

Publisher: Springer

Published: 2014-07-08

Total Pages: 184

ISBN-13: 3319019821

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This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

Book Synopsis Local Minimization, Variational Evolution and Γ-Convergence by : Andrea Braides

Download or read book Local Minimization, Variational Evolution and Γ-Convergence written by Andrea Braides and published by Springer. This book was released on 2014-07-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

Calculus of Variations and Partial Differential Equations

Author: Luigi Ambrosio

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 347

ISBN-13: 3642571867

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At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Book Synopsis Calculus of Variations and Partial Differential Equations by : Luigi Ambrosio

Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Homogenization of Multiple Integrals

Author: Andrea Braides

Publisher: Oxford University Press

Published: 1998

Total Pages: 322

ISBN-13: 9780198502463

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An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.

Book Synopsis Homogenization of Multiple Integrals by : Andrea Braides

Download or read book Homogenization of Multiple Integrals written by Andrea Braides and published by Oxford University Press. This book was released on 1998 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.

Getting Acquainted with Homogenization and Multiscale

Author: Leonid Berlyand

Publisher: Springer

Published: 2018-11-22

Total Pages: 178

ISBN-13: 303001777X

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The 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.

Book Synopsis Getting Acquainted with Homogenization and Multiscale by : Leonid Berlyand

Download or read book Getting Acquainted with Homogenization and Multiscale written by Leonid Berlyand and published by Springer. This book was released on 2018-11-22 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.

The General Theory of Homogenization

Author: Luc Tartar

Publisher: Springer Science & Business Media

Published: 2009-12-03

Total Pages: 466

ISBN-13: 3642051952

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Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

Book Synopsis The General Theory of Homogenization by : Luc Tartar

Download or read book The General Theory of Homogenization written by Luc Tartar and published by Springer Science & Business Media. This book was released on 2009-12-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

Introduction to the Mathematical Theory of Compressible Flow

Author: Antonín Novotny

Publisher: OUP Oxford

Published: 2004-06-17

Total Pages: 528

ISBN-13: 019152395X

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This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.

Book Synopsis Introduction to the Mathematical Theory of Compressible Flow by : Antonín Novotny

Download or read book Introduction to the Mathematical Theory of Compressible Flow written by Antonín Novotny and published by OUP Oxford. This book was released on 2004-06-17 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.