Hyperbolic Conservation Laws and the Compensated Compactness Method, Lu, Yunguang

Автор: Liviu C. Florescu, Christiane Godet-Thobie
Название: Young Measures and Compactness in Measure Spaces
ISBN: 3110276402 ISBN-13(EAN): 9783110276404
Издательство: Walter de Gruyter
Цена: 185890.00 T
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Описание: In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces.The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.

Автор: Luigi Ambrosio; Fabio Ancona; Gianluca Crippa; Ste
Название: Transport Equations and Multi-D Hyperbolic Conservation Laws
ISBN: 3540767800 ISBN-13(EAN): 9783540767800
Издательство: Springer
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Цена: 32560.00 T
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Описание: The theory of nonlinear hyperbolic equations in several space dimensions has obtained many achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This work gives an overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws.

Автор: Cyril Tintarev
Название: Concentration Compactness: Functional-Analytic Theory of Concentration Phenomena
ISBN: 3110530341 ISBN-13(EAN): 9783110530346
Издательство: Walter de Gruyter
Цена: 123910.00 T
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Описание: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jurgen Appell, Wurzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Torun, Poland Vicentiu D. Radulescu, Krakow, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jurgen Appell . Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Автор: Helge Holden; Nils H. Risebro
Название: Front Tracking for Hyperbolic Conservation Laws
ISBN: 3642627978 ISBN-13(EAN): 9783642627972
Издательство: Springer
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Цена: 74530.00 T
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Описание: This book offers a detailed, rigorous, and self-contained presentation of the theory of hyperbolic conservation laws from the basic theory to the forefront of research. The text offers extensive examples, exercises with hints and answers and comprehensive appendices.

Автор: Dafermos
Название: Hyperbolic Conservation Laws in Continuum Physics
ISBN: 3662494493 ISBN-13(EAN): 9783662494493
Издательство: Springer
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Цена: 153720.00 T
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Описание: This is a masterly exposition and an encyclopedicpresentation of the theory of hyperbolic conservation laws. It illustrates theessential role of continuum thermodynamics in providing motivation anddirection for the development of the mathematical theory while also serving asthe principal source of applications. The reader is expected to have a certainmathematical sophistication and to be familiar with (at least) the rudiments ofanalysis and the qualitative theory of partial differential equations, whereasprior exposure to continuum physics is not required. The target group ofreaders would consist of (a) experts in the mathematical theory of hyperbolic systems of conservationlaws 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 mathematicaltheory; and (d) analysts and graduate students who seek introduction to the theory ofhyperbolic systems of conservation laws.This new edition places increased emphasis onhyperbolic systems of balance laws with dissipative source, modeling relaxationphenomena. It also presents an account of recent developments on the Eulerequations of compressible gas dynamics. Furthermore, the presentation of anumber of topics in the previous edition has been revised, expanded andbrought up to date, and has been enriched with new applications toelasticity and differential geometry. The bibliography, also expanded andupdated, now comprises close to two thousand titles.From the reviews of the 3rd edition:'This is the third edition of the famous book byC.M. Dafermos. His masterly written book is, surely, the most completeexposition in the subject.' Evgeniy Panov, Zentralblatt MATH'A monumental book encompassing all aspects ofthe mathematical theory of hyperbolic conservation laws, widely recognized asthe 'Bible' on the subject.' Philippe G. LeFloch, Math. Reviews

Автор: Coron Jean-Michel, Li Ta-Tsien, Li Yachun
Название: One-Dimensional Hyperbolic Conservation Laws and Their Applications
ISBN: 9813276177 ISBN-13(EAN): 9789813276178
Издательство: World Scientific Publishing
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Цена: 137280.00 T
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Описание: This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

Автор: Constantine M. Dafermos
Название: Hyperbolic Conservation Laws in Continuum Physics
ISBN: 3642242421 ISBN-13(EAN): 9783642242427
Издательство: Springer
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Цена: 125770.00 T
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Описание: This presentation of the theory of hyperbolic conservation laws illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory.

Автор: Gui-Qiang G. Chen; Helge Holden; Kenneth H. Karlse
Название: Hyperbolic Conservation Laws and Related Analysis with Applications
ISBN: 3662510987 ISBN-13(EAN): 9783662510988
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications.

Автор: Rainer Ansorge; Hester Bijl; Andreas Meister; Thom
Название: Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
ISBN: 3642437745 ISBN-13(EAN): 9783642437748
Издательство: Springer
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Цена: 241310.00 T
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Описание: This book examines recent developments in the numerics of partial differential equations. It emphasizes methods of high order and applications in computational fluid dynamics.

Автор: Gui-Qiang G. Chen; Helge Holden; Kenneth H. Karlse
Название: Hyperbolic Conservation Laws and Related Analysis with Applications
ISBN: 3642390064 ISBN-13(EAN): 9783642390067
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications.

Автор: Dafermos Constantine M.
Название: Hyperbolic Conservation Laws in Continuum Physics
ISBN: 3662570114 ISBN-13(EAN): 9783662570111
Издательство: Springer
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Цена: 214280.00 T
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Описание: This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws.