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Global Propagation of Regular Nonlinear Hyperbolic Waves

2009-09-01 Science
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Release : 2009-09-01
Genre : Science
Kind : eBook
Book Rating : 353/5 ( reviews)

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Book Synopsis Global Propagation of Regular Nonlinear Hyperbolic Waves by : Tatsien Li

Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li. This book was released on 2009-09-01. 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.

Global Propagation of Regular Nonlinear Hyperbolic Waves

2011-11-02 Science
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Release : 2011-11-02
Genre : Science
Kind : eBook
Book Rating : 686/5 ( reviews)

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Book Synopsis Global Propagation of Regular Nonlinear Hyperbolic Waves by : Tatsien Li

Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li. This book was released on 2011-11-02. 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.

Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 540/5 ( reviews)

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Book Synopsis Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by : Michael Beals

Download or read book Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems written by Michael Beals. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book developed from a series of lectures I gave at the Symposium on Nonlinear Microlocal Analysis held at Nanjing University in October. 1988. Its purpose is to give an overview of the use of microlocal analysis and commutators in the study of solutions to nonlinear wave equations. The weak singularities in the solutions to such equations behave up to a certain extent like those present in the linear case: they propagate along the null bicharacteristics of the operator. On the other hand. examples exhibiting singularities not present in the linear case can also be constructed. I have tried to present a crossection of both the regularity results and the singular examples. for problems on the interior of a domain and on domains with boundary. The main emphasis is on the case of more than one space dimen sion. since that case is treated in great detail in the paper of Rauch-Reed 159]. The results presented here have for the most part appeared elsewhere. and are the work of many authors. but a few new examples and proofs are given. I have attempted to indicate the essential ideas behind the arguments. so that only some of the results are proved in full detail. It is hoped that the central notions of the more technical proofs appearing in research papers will be illuminated by these simpler cases.

Nonlinear Wave Equations

2021-05-30 Mathematics
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Release : 2021-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 724/5 ( reviews)

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Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy. This book was released on 2021-05-30. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Hyperbolic Conservation Laws in Continuum Physics

2016-05-26 Mathematics
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Release : 2016-05-26
Genre : Mathematics
Kind : eBook
Book Rating : 515/5 ( reviews)

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Book Synopsis Hyperbolic Conservation Laws in Continuum Physics by : Constantine M. Dafermos

Download or read book Hyperbolic Conservation Laws in Continuum Physics written by Constantine M. Dafermos. This book was released on 2016-05-26. Available in PDF, EPUB and Kindle. Book excerpt: OLD TEXT 4th Edition to be replaced: This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews

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