Download or read book Cauchy Problem for Quasilinear Hyperbolic Systems written by De-xing Kong and published by . This book was released on 2000-12 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasilinear Hyperbolic Systems And Dissipative Mechanisms written by Ling Hsiao and published by World Scientific. This book was released on 1998-02-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the recent developments in the subject of quasilinear hyperbolic systems with dissipation, such as frictional damping, relaxation, viscosity and heat diffusion. The mathematical theory behind this subject is emphasized in two ways. One emphasis is based on understanding the influence of the dissipation mechanism on the qualitative behavior of solutions, such as the nonlinear diffusive phenomena caused by damping, and other phenomena (including phase transition) for the case with viscosity and heat diffusion. The second emphasis is to take the systems with the dissipation mechanism as an approach to approximating the corresponding system of quasilinear hyperbolic conservation laws - the zero-limit relaxation, or the zero-limit viscosity, and the related topic of nonlinear stability of waves.
Download or read book Applications of Functional Analysis in Mathematical Physics written by S L (Sergeĭ Lʹvovich) 190 Sobolev and published by Hassell Street Press. This book was released on 2021-09-09 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Equations of Evolution written by Hiroki Tanabe and published by Pitman Publishing. This book was released on 1979 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Trends in the Theory of Hyperbolic Equations written by Michael Reissig and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.
Download or read book The Cauchy Problem written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1983 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Download or read book Partial Differential Equations in Classical Mathematical Physics written by Isaak Rubinstein and published by Cambridge University Press. This book was released on 1998-04-28 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Download or read book Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves written by Peter D. Lax and published by SIAM. This book was released on 1973-01-01 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.
Download or read book Systems of Quasilinear Equations and Their Applications to Gas Dynamics written by Boris Leonidovich Rozhdestvenski_ and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by ``Nauka.'' It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.
Download or read book Stability and Boundary Stabilization of 1 D Hyperbolic Systems written by Georges Bastin and published by Birkhäuser. This book was released on 2016-07-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Download or read book Training Manual on Transport and Fluids written by John C. Neu and published by American Mathematical Soc.. This book was released on 2009-11-30 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: I have learned a lot from John Neu over the past years, and his book reflects very well his sense of style and purpose. --Walter Craig, McMaster University, Hamilton, Ontario, Canada and Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada John Neu's book presents the basic ideas of fluid mechanics, and of the transport of matter, in a clear and reader-friendly way. Then it proposes a collection of problems, starting with easy ones and gradually leading up to harder ones. Each problem is solved with all the steps explained. In the course of solving these problems, many fundamental methods of analysis are introduced and explained. This is an ideal book for use as a text, or for individual study. --Joseph B. Keller, Stanford University This book presents elementary models of transport in continuous media and a corresponding body of mathematical technique. Physical topics include convection and diffusion as the simplest models of transport; local conservation laws with sources as the general framework of continuum mechanics; ideal fluid as the simplest model of a medium with mass; momentum and energy transport; and finally, free surface waves, in particular, shallow water theory. There is a strong emphasis on dimensional analysis and scaling. Some topics, such as physical similarity and similarity solutions, are traditional. In addition, there are reductions based on scaling, such as incompressible flow as a limit of compressible flow, and shallow water theory derived asymptotically from the full equations of free surface waves. More and deeper examples are presented as problems, including a series of problems that model a tsunami approaching the shore. The problems form an embedded subtext to the book. Each problem is followed by a detailed solution emphasizing process and craftsmanship. The problems express the practice of applied mathematics as the examination and re-examination of simple but essential ideas in many interrelated examples.
Download or read book Blowup for Nonlinear Hyperbolic Equations written by Serge Alinhac and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as blowup. In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it.
Download or read book Proceedings of the Ninth International Colloquium on Differential Equations written by D. Bainov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-02-11 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Nonlinear Evolution Systems written by Jerome and published by Academic Press. This book was released on 1983-04-22 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation of Nonlinear Evolution Systems
Download or read book Partial Differential Equations written by Phoolan Prasad and published by New Age International. This book was released on 1985 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.
Download or read book Hyperbolic Partial Differential Equations written by Serge Alinhac and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
