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Hyperbolic Conservation Laws In Continuum Physics

Author: Constantine M. Dafermos
Publisher: Springer
ISBN: 3662494515
Size: 47.28 MB
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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

Hyperbolic Conservation Laws In Continuum Physics

Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3540290893
Size: 79.10 MB
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This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH

Numerical Methods For Conservation Laws

Author: Jan S. Hesthaven
Publisher: SIAM
ISBN: 1611975093
Size: 57.79 MB
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Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.

Hyperbolic Systems Of Balance Laws

Author: Alberto Bressan
Publisher: Springer
ISBN: 3540721878
Size: 48.85 MB
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This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

Quasilinear Hyperbolic Systems Compressible Flows And Waves

Author: Vishnu D. Sharma
Publisher: CRC Press
ISBN: 9781439836910
Size: 28.86 MB
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Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications. It emphasizes nonlinear theory and introduces some of the most active research in the field. After linking continuum mechanics and quasilinear partial differential equations, the book discusses the scalar conservation laws and hyperbolic systems in two independent variables. Using the method of characteristics and singular surface theory, the author then presents the evolutionary behavior of weak and mild discontinuities in a quasilinear hyperbolic system. He also explains how to apply weakly nonlinear geometrical optics in nonequilibrium and stratified gas flows and demonstrates the power, generality, and elegance of group theoretic methods for solving Euler equations of gasdynamics involving shocks. The final chapter deals with the kinematics of a shock of arbitrary strength in three dimensions. With a focus on physical applications, this text takes readers on a journey through this fascinating area of applied mathematics. It provides the essential mathematical concepts and techniques to understand the phenomena from a theoretical standpoint and to solve a variety of physical problems.

Hyperbolic Problems

Author: Eitan Tadmor
Publisher: Amer Mathematical Society
ISBN:
Size: 75.10 MB
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'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. The articles in this two-part volume are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.

Metastability

Author: Anton Bovier
Publisher: Springer
ISBN: 3319247778
Size: 67.45 MB
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This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.