Homogenization Of Partial Differential Equations

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Homogenization Of Partial Differential Equations

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Author : Vladimir A. Marchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006

Homogenization Of Partial Differential Equations written by Vladimir A. Marchenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Language Arts & Disciplines categories.

A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers

Homogenization Of Partial Differential Equations

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Author : Vladimir A. Marchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22

Homogenization Of Partial Differential Equations written by Vladimir A. Marchenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-22 with Mathematics categories.

Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory. Along with complete proofs of all main results, numerous examples of typical structures of microinhomogeneous media with their corresponding homogenized models are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.

Emerging Problems In The Homogenization Of Partial Differential Equations

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Author : Patrizia Donato
language : en
Publisher: Springer Nature
Release Date : 2021-02-01

Emerging Problems In The Homogenization Of Partial Differential Equations written by Patrizia Donato and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-01 with Mathematics categories.

This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.

Emerging Problems In The Homogenization Of Partial Differential Equations

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Author : Patrizia Donato
language : en
Publisher:
Release Date : 2021

Emerging Problems In The Homogenization Of Partial Differential Equations written by Patrizia Donato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors. .

Homogenization Of Partial Differential Equations With Uncertain Input Data

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Author : Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky
language : en
Publisher:
Release Date : 2013

Homogenization Of Partial Differential Equations With Uncertain Input Data written by Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Homogenization Of Partial Differential Equations With Random Large Potential

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Author : Ningyao Zhang
language : en
Publisher:
Release Date : 2013

Homogenization Of Partial Differential Equations With Random Large Potential written by Ningyao Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.

Partial differential equations with highly oscillatory, random coefficients describe many applications in applied science and engineering such as porous media and composite materials. Homogenization of PDE states that the solution of the initial model converges to the solution to a macro model, which is characterized by the PDE with homogenized coefficients. Particularly, we study PDEs with a large potential, a class of PDEs with a potential properly scaled such that the limiting equation has a non-trivial (non-zero) potential. This thesis consists of the investigation of three issues. The first issue is the convergence of Schodinger equation to a deterministic homogenized PDE in high dimension. The second issue is the convergence of the same equation to a stochastic PDE in low dimension. The third issue is the convergence of elliptic equation with an imaginary potential.

Calculus Of Variations And Nonlinear Partial Differential Equations

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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02

Calculus Of Variations And Nonlinear Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-02 with Mathematics categories.

With a historical overview by Elvira Mascolo

Homogenization Of Differential Operators And Integral Functionals

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Author : V.V. Jikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Homogenization Of Differential Operators And Integral Functionals written by V.V. Jikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

G Convergence And Homogenization Of Nonlinear Partial Differential Operators

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Author : A. A. Pankov
language : en
Publisher:
Release Date : 2014-01-15

G Convergence And Homogenization Of Nonlinear Partial Differential Operators written by A. A. Pankov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Effective Dynamics Of Stochastic Partial Differential Equations

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Author : Jinqiao Duan
language : en
Publisher: Elsevier
Release Date : 2014-03-06

Effective Dynamics Of Stochastic Partial Differential Equations written by Jinqiao Duan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-06 with Mathematics categories.

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises