Classically Unstable Approximations For Linear Evolution Equations And Applications
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Author |
: Yu Zhuang |
Publisher |
: |
Total Pages |
: 174 |
Release |
: 2000 |
ISBN-10 |
: OCLC:44804484 |
ISBN-13 |
: |
Rating |
: 4/5 (84 Downloads) |
Synopsis Classically Unstable Approximations for Linear Evolution Equations and Applications by : Yu Zhuang
Author |
: Kazufumi Ito |
Publisher |
: World Scientific |
Total Pages |
: 518 |
Release |
: 2002-05-24 |
ISBN-10 |
: 9789814488389 |
ISBN-13 |
: 9814488380 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Evolution Equations And Approximations by : Kazufumi Ito
This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and the Lie-Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory.In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.
Author |
: Michael Demuth |
Publisher |
: Birkhäuser |
Total Pages |
: 346 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034882316 |
ISBN-13 |
: 3034882319 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Partial Differential Equations and Spectral Theory by : Michael Demuth
The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
Author |
: Tatsien Li |
Publisher |
: World Scientific |
Total Pages |
: 274 |
Release |
: 1991-11-29 |
ISBN-10 |
: 9789814569385 |
ISBN-13 |
: 9814569380 |
Rating |
: 4/5 (85 Downloads) |
Synopsis Qualitative Aspects And Applications Of Nonlinear Evolution Equations - Proceedings Of The School by : Tatsien Li
Author |
: Pascal Cherrier |
Publisher |
: Springer |
Total Pages |
: 155 |
Release |
: 2015-10-12 |
ISBN-10 |
: 9783319209975 |
ISBN-13 |
: 3319209973 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Evolution Equations of von Karman Type by : Pascal Cherrier
In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a deeper insight into the power of nontrivial a priori estimate methods in the qualitative study of nonlinear differential equations.
Author |
: |
Publisher |
: |
Total Pages |
: 816 |
Release |
: 2000 |
ISBN-10 |
: UOM:39015086908152 |
ISBN-13 |
: |
Rating |
: 4/5 (52 Downloads) |
Synopsis American Doctoral Dissertations by :
Author |
: J. R. Mika |
Publisher |
: World Scientific |
Total Pages |
: 332 |
Release |
: 1995 |
ISBN-10 |
: 9810221258 |
ISBN-13 |
: 9789810221256 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Singularly Perturbed Evolution Equations with Applications to Kinetic Theory by : J. R. Mika
In recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.
Author |
: Jerome |
Publisher |
: Academic Press |
Total Pages |
: 301 |
Release |
: 1983-04-22 |
ISBN-10 |
: 9780080956701 |
ISBN-13 |
: 008095670X |
Rating |
: 4/5 (01 Downloads) |
Synopsis Approximation of Nonlinear Evolution Systems by : Jerome
Approximation of Nonlinear Evolution Systems
Author |
: Niels Benedikter |
Publisher |
: Springer |
Total Pages |
: 97 |
Release |
: 2015-11-04 |
ISBN-10 |
: 9783319248981 |
ISBN-13 |
: 3319248987 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Effective Evolution Equations from Quantum Dynamics by : Niels Benedikter
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 |
: Behzad Djafari Rouhani |
Publisher |
: CRC Press |
Total Pages |
: 205 |
Release |
: 2019-05-20 |
ISBN-10 |
: 9780429528880 |
ISBN-13 |
: 0429528884 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces by : Behzad Djafari Rouhani
This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.