Topological Approximation Methods For Evolutionary Problems Of Nonlinear Hydrodynamics
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Topological Approximation Methods For Evolutionary Problems Of Nonlinear Hydrodynamics
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Author : Victor G. Zvyagin
language : en
Publisher: Walter de Gruyter
Release Date : 2008-09-25
Topological Approximation Methods For Evolutionary Problems Of Nonlinear Hydrodynamics written by Victor G. Zvyagin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-25 with Mathematics categories.
The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
Blow Up In Nonlinear Equations Of Mathematical Physics
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Author : Maxim Olegovich Korpusov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Blow Up In Nonlinear Equations Of Mathematical Physics written by Maxim Olegovich Korpusov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Mathematics categories.
The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results
Functional Analysis In Interdisciplinary Applications Ii
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Author : Allaberen Ashyralyev
language : en
Publisher: Springer Nature
Release Date : 2021-07-03
Functional Analysis In Interdisciplinary Applications Ii written by Allaberen Ashyralyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-03 with Mathematics categories.
Functional analysis is an important branch of mathematical analysis which deals with the transformations of functions and their algebraic and topological properties. Motivated by their large applicability to real life problems, applications of functional analysis have been the aim of an intensive study effort in the last decades, yielding significant progress in the theory of functions and functional spaces, differential and difference equations and boundary value problems, differential and integral operators and spectral theory, and mathematical methods in physical and engineering sciences. The present volume is devoted to these investigations. The publication of this collection of papers is based on the materials of the mini-symposium "Functional Analysis in Interdisciplinary Applications" organized in the framework of the Fourth International Conference on Analysis and Applied Mathematics (ICAAM 2018, September 6–9, 2018). Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis. Many articles are written by experts from around the world, strengthening international integration in the fields covered. The contributions to the volume, all peer reviewed, contain numerous new results. This volume contains four different chapters. The first chapter contains the contributed papers focusing on various aspects of the theory of functions and functional spaces. The second chapter is devoted to the research on difference and differential equations and boundary value problems. The third chapter contains the results of studies on differential and integral operators and on the spectral theory. The fourth chapter is focused on the simulation of problems arising in real-world applications of applied sciences.
Infinite Dimensional Dynamical Systems
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Author : John Mallet-Paret
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-11
Infinite Dimensional Dynamical Systems written by John Mallet-Paret 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 2012-10-11 with Mathematics categories.
This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation and applications of new developments of nonlinear analysis and other mathematical theories. Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects the pioneering work and influence of Professor Sell in a few core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Spde In Hydrodynamics Recent Progress And Prospects
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-14
Spde In Hydrodynamics Recent Progress And Prospects written by Sergio Albeverio 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 2008-04-14 with Mathematics categories.
Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda 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 2013-03-09 with Science categories.
Many physical systems lose or gain stability and pattern through bifurca tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of im perfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as im perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis tical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection.
Optimization In Solving Elliptic Problems
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Author : Eugene G. D'yakonov
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Optimization In Solving Elliptic Problems written by Eugene G. D'yakonov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema
Physics Uspekhi
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Author :
language : en
Publisher:
Release Date : 2005
Physics Uspekhi written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Physics categories.
Dynamics Of Evolutionary Equations
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Author : George R. Sell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Dynamics Of Evolutionary Equations written by George R. Sell 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 2013-04-17 with Mathematics categories.
The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.