G Convergence And Homogenization Of Nonlinear Partial Differential Operators PDF Download
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Author | : A. A. Pankov |
Publisher | : |
Total Pages | : 278 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789401589581 |
Download G-Convergence and Homogenization of Nonlinear Partial Differential Operators Book in PDF, ePub and Kindle
Author | : A.A. Pankov |
Publisher | : Springer Science & Business Media |
Total Pages | : 269 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401589577 |
Download G-Convergence and Homogenization of Nonlinear Partial Differential Operators Book in PDF, ePub and Kindle
Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.
Author | : A.A. Pankov |
Publisher | : Springer Science & Business Media |
Total Pages | : 276 |
Release | : 1997-09-30 |
Genre | : Mathematics |
ISBN | : 9780792347200 |
Download G-Convergence and Homogenization of Nonlinear Partial Differential Operators Book in PDF, ePub and Kindle
Various applications of the homogenization theory of partial differential equations resulted in the further development of this branch of mathematics, attracting an increasing interest of both mathematicians and experts in other fields. In general, the theory deals with the following: Let Ak be a sequence of differential operators, linear or nonlinepr. We want to examine the asymptotic behaviour of solutions uk to the equation Auk = f, as k ~ =, provided coefficients of Ak contain rapid oscillations. This is the case, e. g. when the coefficients are of the form a(e/x), where the function a(y) is periodic and ek ~ 0 ask~=. Of course, of oscillation, like almost periodic or random homogeneous, are of many other kinds interest as well. It seems a good idea to find a differential operator A such that uk ~ u, where u is a solution of the limit equation Au = f Such a limit operator is usually called the homogenized operator for the sequence Ak . Sometimes, the term "averaged" is used instead of "homogenized". Let us look more closely what kind of convergence one can expect for uk. Usually, we have some a priori bound for the solutions. However, due to the rapid oscillations of the coefficients, such a bound may be uniform with respect to k in the corresponding energy norm only. Therefore, we may have convergence of solutions only in the weak topology of the energy space.
Author | : Vasiliĭ Vasilʹevich Zhikov |
Publisher | : Springer |
Total Pages | : 592 |
Release | : 1994 |
Genre | : Continuum mechanics |
ISBN | : |
Download Homogenization of Differential Operators and Integral Functionals Book in PDF, ePub and Kindle
This extensive study of the theory of the homogenization of partial differential equations explores solutions to the problems which arise in mathematics, science and engineering. The reference aims to provide the basis for new research devoted to these problems.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Homogenization of Nonlinear Partial Differential Operators Book in PDF, ePub and Kindle
Author | : V. Lakshmikantham |
Publisher | : CRC Press |
Total Pages | : 328 |
Release | : 2003-02-27 |
Genre | : Mathematics |
ISBN | : 1482288273 |
Download Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combin
Author | : Patrizia Donato |
Publisher | : Springer Nature |
Total Pages | : 122 |
Release | : 2021-02-01 |
Genre | : Mathematics |
ISBN | : 3030620301 |
Download Emerging Problems in the Homogenization of Partial Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Gianni Dal Maso |
Publisher | : Springer Science & Business Media |
Total Pages | : 351 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203279 |
Download An Introduction to Γ-Convergence Book in PDF, ePub and Kindle
Author | : Luc Tartar |
Publisher | : Springer Science & Business Media |
Total Pages | : 466 |
Release | : 2009-12-03 |
Genre | : Science |
ISBN | : 3642051952 |
Download The General Theory of Homogenization Book in PDF, ePub and Kindle
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.
Author | : Doina Cioranescu |
Publisher | : Elsevier |
Total Pages | : 665 |
Release | : 2002-06-21 |
Genre | : Mathematics |
ISBN | : 0080537677 |
Download Nonlinear Partial Differential Equations and Their Applications Book in PDF, ePub and Kindle
This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.