Evolution Equations And Approximations PDF Download
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Author | : Kazufumi Ito |
Publisher | : World Scientific |
Total Pages | : 524 |
Release | : 2002 |
Genre | : Science |
ISBN | : 9789812380265 |
Download Evolution Equations and Approximations Book in PDF, ePub and Kindle
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Raphael Kruse |
Publisher | : Springer |
Total Pages | : 177 |
Release | : 2013-11-18 |
Genre | : Mathematics |
ISBN | : 3319022318 |
Download Strong and Weak Approximation of Semilinear Stochastic Evolution Equations Book in PDF, ePub and Kindle
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Author | : Jerome |
Publisher | : Academic Press |
Total Pages | : 279 |
Release | : 1983-04-22 |
Genre | : Computers |
ISBN | : 008095670X |
Download Approximation of Nonlinear Evolution Systems Book in PDF, ePub and Kindle
Approximation of Nonlinear Evolution Systems
Author | : Niels Benedikter |
Publisher | : Springer |
Total Pages | : 91 |
Release | : 2015-11-04 |
Genre | : Science |
ISBN | : 3319248987 |
Download Effective Evolution Equations from Quantum Dynamics Book in PDF, ePub and Kindle
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.
Author | : T. E. Govindan |
Publisher | : Springer |
Total Pages | : 407 |
Release | : 2016-11-11 |
Genre | : Mathematics |
ISBN | : 3319456849 |
Download Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications Book in PDF, ePub and Kindle
This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use. This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.
Author | : T. E. Govindan |
Publisher | : Springer Nature |
Total Pages | : 321 |
Release | : |
Genre | : |
ISBN | : 3031427912 |
Download Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications Book in PDF, ePub and Kindle
Author | : G F Roach |
Publisher | : CRC Press |
Total Pages | : 268 |
Release | : 1995-04-28 |
Genre | : Mathematics |
ISBN | : 9780582246690 |
Download Recent Developments in Evolution Equations Book in PDF, ePub and Kindle
This book presents the majority of talks given at an International Converence held recently at the University of Strathclyde in Glasgow. The works presented focus on the analysis of mathematical models of systems evolving with time. The main topics are semigroups and related subjects connected with applications to partial differential equations of evolution type. Topics of particular interest include spectral and asymptotic properties of semigroups, B evolution scattering theory, and coagulation fragmentation phenomena.
Author | : Yong Zhou |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 255 |
Release | : 2022-03-21 |
Genre | : Technology & Engineering |
ISBN | : 3110769360 |
Download Theory of Fractional Evolution Equations Book in PDF, ePub and Kindle
Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.
Author | : Mimmo Iannelli |
Publisher | : Birkhäuser |
Total Pages | : 419 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880855 |
Download Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics Book in PDF, ePub and Kindle
The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.
Author | : David Ellwood |
Publisher | : American Mathematical Soc. |
Total Pages | : 587 |
Release | : 2013-06-26 |
Genre | : Mathematics |
ISBN | : 0821868616 |
Download Evolution Equations Book in PDF, ePub and Kindle
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).