Shock Waves And Reaction Diffusion Equations

Author : Joel Smoller
Publisher : Springer Science & Business Media
Page : 650 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208730

Get Book

Shock Waves and Reaction—Diffusion Equations by Joel Smoller Pdf

For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.

Author : Joel Smoller
Publisher : Unknown
Page : 632 pages
File Size : 52,6 Mb
Release : 1994-01-01
Category : Ondes de choc
ISBN : 3540942599

Get Book

Shock Waves and Reaction-diffusion Equations by Joel Smoller Pdf

Author : J. Smoller
Publisher : Springer
Page : 0 pages
File Size : 42,6 Mb
Release : 2012
Category : Acoustics
ISBN : 1468401548

Get Book

Shock Waves and Reaction-Diffusion Equations by J. Smoller Pdf

... The progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations ... and therefore we can learn by comparing different nonlinear problems. WERNER HEISENBERG I undertook to write this book for two reasons. First, I wanted to make easily available the basics of both the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by C. Conley. These important subjects seem difficult to learn since the results are scattered throughout the research journals. 1 Second, I feel that there is a need to present the modern methods and ideas in these fields to a wider audience than just mathe maticians. Thus, the book has some rather sophisticated aspects to it, as well as certain textbook aspects. The latter serve to explain, somewhat, the reason that a book with the title Shock Waves and Reaction-Diffusion Equations has the first nine chapters devoted to linear partial differential equations. More precisely, I have found from my classroom experience that it is far easier to grasp the subtleties of nonlinear partial differential equations after one has an understanding of the basic notions in the linear theory. This book is divided into four main parts: linear theory, reaction diffusion equations, shock wave theory, and the Conley index, in that order. Thus, the text begins with a discussion of ill-posed problems.

Author : Peter Grindrod
Publisher : Oxford University Press
Page : 275 pages
File Size : 42,5 Mb
Release : 1996
Category : Mathematics
ISBN : 0198500041

Get Book

The Theory and Applications of Reaction-diffusion Equations by Peter Grindrod Pdf

This textbook is concerned with the highly topical area of reaction-diffusion equations. This popular textbook provides a compendium of useful techniques for the analysis of such equations and shows how they find application in a variety of settings, notably in pattern formation and nonplanar wave-like structures. New to the second edition, is a chapter on geochemical systems with applications to environmental modelling problems. This is an ideal introduction to the subject for graduatestudents as well as those mathematicians and scientists whose work touches on these topics.

Author : Peter Grindrod
Publisher : Unknown
Page : 275 pages
File Size : 42,7 Mb
Release : 1996
Category : Reaction-diffusion equations
ISBN : OCLC:262718390

Get Book

Patterns and Waves by Peter Grindrod Pdf

Author : Jeffrey Groah,Joel Smoller,Blake Temple
Publisher : Springer Science & Business Media
Page : 152 pages
File Size : 51,9 Mb
Release : 2007-04-03
Category : Mathematics
ISBN : 9780387446028

Get Book

Shock Wave Interactions in General Relativity by Jeffrey Groah,Joel Smoller,Blake Temple Pdf

This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The author is a well regarded expert in this area.

Author : Andreas Liehr
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 44,8 Mb
Release : 2013-03-27
Category : Science
ISBN : 9783642312519

Get Book

Dissipative Solitons in Reaction Diffusion Systems by Andreas Liehr Pdf

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Author : Gabi Ben-Dor,Ozer Igra,Tov Elperin
Publisher : Elsevier
Page : 2188 pages
File Size : 44,5 Mb
Release : 2000-10-18
Category : Science
ISBN : 9780080533728

Get Book

Handbook of Shock Waves, Three Volume Set by Gabi Ben-Dor,Ozer Igra,Tov Elperin Pdf

The Handbook of Shock Waves contains a comprehensive, structured coverage of research topics related to shock wave phenomena including shock waves in gases, liquids, solids, and space. Shock waves represent an extremely important physical phenomena which appears to be of special practical importance in three major fields: compressible flow (aerodynamics), materials science, and astrophysics. Shock waves comprise a phenomenon that occurs when pressure builds to force a reaction, i.e. sonic boom that occurs when a jet breaks the speed of sound.This Handbook contains experimental, theoretical, and numerical results which never before appeared under one cover; the first handbook of its kind.The Handbook of Shock Waves is intended for researchers and engineers active in shock wave related fields. Additionally, R&D establishments, applied science & research laboratories and scientific and engineering libraries both in universities and government institutions. As well as, undergraduate and graduate students in fluid mechanics, gas dynamics, and physics. Key Features* Ben-Dor is known as one of the founders of the field of shock waves* Covers a broad spectrum of shock wave research topics* Provides a comprehensive description of various shock wave related subjects* First handbook ever to include under one separate cover: experimental, theoretical, and numerical results

Author : Heinrich Freistühler,Anders Szepessy
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201939

Get Book

Advances in the Theory of Shock Waves by Heinrich Freistühler,Anders Szepessy Pdf

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

Author : A. I. Volpert,Vitaly A. Volpert,Vladimir A. Volpert
Publisher : American Mathematical Soc.
Page : 474 pages
File Size : 46,6 Mb
Release : 2024-05-04
Category : Mathematics
ISBN : 0821897578

Get Book

Traveling Wave Solutions of Parabolic Systems by A. I. Volpert,Vitaly A. Volpert,Vladimir A. Volpert Pdf

The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.

Author : Mark I. Freidlin,Sergey Gredeskul,John K. Hunter,Andrew Marchenko,Leonid Pastur
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461519911

Get Book

Surveys in Applied Mathematics by Mark I. Freidlin,Sergey Gredeskul,John K. Hunter,Andrew Marchenko,Leonid Pastur Pdf

Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.

Author : Christian Klingenberg,Michael Westdickenberg
Publisher : Springer
Page : 714 pages
File Size : 53,7 Mb
Release : 2018-06-27
Category : Mathematics
ISBN : 9783319915487

Get Book

Theory, Numerics and Applications of Hyperbolic Problems II by Christian Klingenberg,Michael Westdickenberg Pdf

The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Author : Tai-Ping Liu
Publisher : American Mathematical Soc.
Page : 437 pages
File Size : 44,8 Mb
Release : 2021-10-12
Category : Education
ISBN : 9781470466251

Get Book

Shock Waves by Tai-Ping Liu Pdf

This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws. The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters. The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.

Author : John Von Neumann,F. Br¢dy,Tibor V mos
Publisher : World Scientific
Page : 768 pages
File Size : 40,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9810222017

Get Book

The Neumann Compendium by John Von Neumann,F. Br¢dy,Tibor V mos Pdf

After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In addition, one paper which was written in German will be translated and published in English for the first time.The sections are introduced by short explanatory notes with an emphasis on recent developments based on von Neumann's contributions. An overall picture is provided by Ulam's, one of his most intimate partners in thinking, 1958 memorial lecture. Facsimilae and translations of some of his personal letters and a newly completed bibliography based on von Neumann's own careful compilation are added.

Author : W.Y. Tan
Publisher : Elsevier
Page : 433 pages
File Size : 46,9 Mb
Release : 1992-08-17
Category : Science
ISBN : 0080870937

Get Book

Shallow Water Hydrodynamics by W.Y. Tan Pdf

Within this monograph a comprehensive and systematic knowledge on shallow-water hydrodynamics is presented. A two-dimensional system of shallow-water equations is analyzed, including the mathematical and mechanical backgrounds, the properties of the system and its solution. Also featured is a new mathematical simulation of shallow-water flows by compressible plane flows of a special virtual perfect gas, as well as practical algorithms such as FDM, FEM, and FVM. Some of these algorithms have been utilized in solving the system, while others have been utilized in various applied fields. An emphasis has been placed on several classes of high-performance difference schemes and boundary procedures which have found wide uses recently for solving the Euler equations of gas dynamics in aeronautical and aerospatial engineering. This book is constructed so that it may serve as a handbook for practicians. It will be of interest to scientists, designers, teachers, postgraduates and professionals in hydraulic, marine, and environmental engineering; especially those involved in the mathematical modelling of shallow-water bodies.