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Local minimization, variational evolution and Γ-convergence

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...

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Detalles Bibliográficos
Autor principal: Braides, Andrea
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-01982-6
http://cds.cern.ch/record/1690665
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author Braides, Andrea
author_facet Braides, Andrea
author_sort Braides, Andrea
collection CERN
description 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.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-16906652021-04-21T21:14:11Zdoi:10.1007/978-3-319-01982-6http://cds.cern.ch/record/1690665engBraides, AndreaLocal minimization, variational evolution and Γ-convergenceMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:16906652014
spellingShingle Mathematical Physics and Mathematics
Braides, Andrea
Local minimization, variational evolution and Γ-convergence
title Local minimization, variational evolution and Γ-convergence
title_full Local minimization, variational evolution and Γ-convergence
title_fullStr Local minimization, variational evolution and Γ-convergence
title_full_unstemmed Local minimization, variational evolution and Γ-convergence
title_short Local minimization, variational evolution and Γ-convergence
title_sort local minimization, variational evolution and γ-convergence
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-01982-6
http://cds.cern.ch/record/1690665
work_keys_str_mv AT braidesandrea localminimizationvariationalevolutionandgconvergence