Systèmes de lois de conservation et stabilité BV PDF Download
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Author: Christophe Cheverry
Publisher: Societe Mathematique De France
ISBN: 9782856290729
Category : Foreign Language Study
Languages : fr
Pages : 106
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Book Description
Author: Christophe Cheverry
Publisher: Societe Mathematique De France
ISBN: 9782856290729
Category : Foreign Language Study
Languages : fr
Pages : 106
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Book Description
Author: Philippe G. LeFloch
Publisher: Birkhäuser
ISBN: 3034881509
Category : Mathematics
Languages : en
Pages : 301
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Book Description
This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
Author: Alberto Bressan
Publisher: Oxford University Press, USA
ISBN: 9780198507000
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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 very recent 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 volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.
Author: Alberto Bressan
Publisher: Springer Science & Business Media
ISBN: 1441995544
Category : Mathematics
Languages : en
Pages : 487
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Book Description
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
Author: Luigi Ambrosio
Publisher: Springer
ISBN: 3642321607
Category : Mathematics
Languages : en
Pages : 507
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Book Description
In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.
Author: Ferrucio Colombini
Publisher: Springer Science & Business Media
ISBN: 1461220149
Category : Mathematics
Languages : en
Pages : 365
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Book Description
This book contains fourteen research papers which are expanded versions of conferences given at a meeting held in September 1996 in Cortona, Italy. The topics include blowup questions for quasilinear equations in two dimensions, time decay of waves in LP, uniqueness results for systems of conservation laws in one dimension, concentra tion effects for critical nonlinear wave equations, diffraction of nonlin ear waves, propagation of singularities in scattering theory, caustics for semi-linear oscillations. Other topics linked to microlocal analysis are Sobolev embedding theorems in Weyl-Hormander calculus, local solv ability for pseudodifferential equations, hypoellipticity for highly degen erate operators. The book also contains a result on uniqueness for the Cauchy problem under partial analyticity assumptions and an article on the regularity of solutions for characteristic initial-boundary value problems. On each topic listed above, one will find new results as well as a description of the state of the art. Various methods related to nonlinear geometrical optics are a transversal theme of several articles. Pseu dodifferential techniques are used to tackle classical PDE problems like Cauchy uniqueness. We are pleased to thank the speakers for their contributions to the meeting: Serge Alinhac, Mike Beals, Alberto Bressan, Jean-Yves Chemin, Christophe Cheverry, Daniele Del Santo, Nils Dencker, Patrick Gerard, Lars Hormander, John Hunter, Richard Melrose, Guy Metivier, Yoshinori Morimoto, and Tatsuo Nishitani. The meeting was made possible in part by the financial support of a European commission pro gram, "Human capital and mobility CHRX-CT94-044."
Author: Constantine M. Dafermos
Publisher: Springer Science & Business Media
ISBN: 3540290893
Category : Mathematics
Languages : en
Pages : 636
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Book Description
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
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 546
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 680
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Book Description
Author: Michael Harris
Publisher:
ISBN:
Category : Hodge theory
Languages : en
Pages : 132
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Book Description
In this book, the authors complete the verification of the following fact: The nerve spectral sequence for the cohomology of the Borel-Serre boundary of a Shimura variety $\mathrm{Sh}$ is a spectral sequence of mixed Hodge-de Rham structures over the field of definition of its canonical model. To achieve that, they develop the machinery of automorphic vector bundles on mixed Shimura varieties, for the latter enter in the boundary of the toroidal compactifications of $\mathrm{Sh}$; and study the nerve spectral sequence for the automorphic vector bundles and the toroidal boundary. They also extend the technique of averting issues of base-change by taking cohomology with growth conditions. They give and apply formulas for the Hodge gradation of the cohomology of both $\mathrm{Sh}$ and its Borel-Serre boundary.
