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Author: Luís Barreira
Publisher: Springer
ISBN: 3319901109
Category : Mathematics
Languages : en
Pages : 153
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Book Description
This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part.
Author: Luís Barreira
Publisher: Springer
ISBN: 3319901109
Category : Mathematics
Languages : en
Pages : 153
Get Book Here
Book Description
This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part.
Author: Luis Barreira
Publisher: World Scientific
ISBN: 9811230269
Category : Mathematics
Languages : en
Pages : 241
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Book Description
This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms.The book is dedicated to researchers as well as graduate students specializing in differential equations and dynamical systems who wish to have an extensive and in-depth view of the hyperbolicity theory of delay equations. It can also be used as a basis for graduate courses on the stability and hyperbolicity of delay equations.
Author: Heinrich Freistühler
Publisher: Birkhäuser
ISBN: 3034883722
Category : Mathematics
Languages : en
Pages : 471
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Book Description
Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.
Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3642040489
Category : Mathematics
Languages : en
Pages : 710
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Book Description
The 3rd edition is thoroughly revised, applications are substantially enriched, it includes a new account of the early history of the subject (from 1800 to 1957) and a new chapter recounting the recent solution of open problems of long standing in classical aerodynamics. The bibliography comprises now over fifteen hundred titles. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH
Author: Andras Batkai
Publisher: CRC Press
ISBN: 143986568X
Category : Mathematics
Languages : en
Pages : 272
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Book Description
In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential equations with delay. This book presents, in a systematic fashion, how delay equations can be studied
Author: Remi Abgrall
Publisher: Elsevier
ISBN: 0444637958
Category : Mathematics
Languages : en
Pages : 668
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Book Description
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage
Author: Claude Carasso
Publisher: Springer
ISBN: 3540478051
Category : Mathematics
Languages : en
Pages : 356
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Book Description
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.
Author: Josef Ballmann
Publisher: Springer Science & Business Media
ISBN: 3322878694
Category : Technology & Engineering
Languages : en
Pages : 729
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Book Description
On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.
Author: Song Jiang
Publisher: World Scientific
ISBN: 9814417092
Category : Mathematics
Languages : en
Pages : 793
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Book Description
This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."
Author: Gui-Qiang G. Chen
Publisher: Springer Science & Business Media
ISBN: 3642390072
Category : Mathematics
Languages : en
Pages : 390
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Book Description
This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation. Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model. The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students interested in partial differential equations and related analysis with applications.
