Hyperbolic Systems of Conservation Laws: The one-dimensional Cauchy problem

Hardcover | June 16, 2003

byAlberto Bressan

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This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in veryrecent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This monograph is the first to present acomprehensive account of these new, fundamental advances, mainly obtained by the author together with several collaborators. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. The book is addressed to graduate students as well as researchers.Both the elementary and the more advanced material are carefully explained, helping the reader's visual intuition with over 70 figures. A set of problems, with varying difficulty, is given at the end of each chapter. These exercises are designed to verify and expand a student's understanding ofthe concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference for the state of the art, in the field of hyperbolic systems of conservation laws. The last chapter contains a large, up to date list of references, preceded by extensivebibliographical notes.

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This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in veryrecent years thanks to the introduction of new t...

Alberto Bressan is at SISSA, Trieste.

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Format:HardcoverPublished:June 16, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198507003

ISBN - 13:9780198507000

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"Hyperbolic systems of conservation laws has become such a mature topic in the past decade that several researchers decided to write a book on the subject recently. . This book is entirely devoted to the achievements of the author's long-standing program. The author's results have been the mostimpressive obtained about conservation laws in the past decade. . .Bressan's style is fluid, and several exercises help doctoral students to digest each chapter. . .Presumably, this book will be often cited in research papers on hyperbolic conservation laws. It is recommended to researchers andgraduate students who specialize in this field."--Mathematical Review