Nonlinear Hyperbolic Problems

Author : Michael Beals
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461245544

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Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems by Michael Beals Pdf

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.

Author : Claude Carasso,Pierre-Arnaud Raviart,Denis Serre
Publisher : Springer
Page : 356 pages
File Size : 48,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540478058

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre-Arnaud Raviart,Denis Serre Pdf

The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

Author : Claude Carasso,Pierre Charrier,Bernard Hanouzet,Jean-Luc Joly
Publisher : Springer
Page : 254 pages
File Size : 54,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468004

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre Charrier,Bernard Hanouzet,Jean-Luc Joly Pdf

The papers included in this proceedings volume are mostly original research papers, dealing with life-span of waves, nonlinear interaction of waves, and various applications to fluid mechanics.

Author : Andrea Donato,Francesco Oliveri
Publisher : Springer Science & Business Media
Page : 623 pages
File Size : 50,9 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9783322878717

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Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects by Andrea Donato,Francesco Oliveri Pdf

Author : Claude Carasso,Pierre Charrier,Bernard Hanouzet
Publisher : Unknown
Page : 266 pages
File Size : 48,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662170795

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Nonlinear Hyperbolic Problems by Claude Carasso,Pierre Charrier,Bernard Hanouzet Pdf

Author : Yuejun Peng,Bopeng Rao
Publisher : World Scientific
Page : 464 pages
File Size : 53,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814322881

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Some Problems on Nonlinear Hyperbolic Equations and Applications by Yuejun Peng,Bopeng Rao Pdf

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Author : Josef Ballmann,Rolf Jeltsch
Publisher : Springer Science & Business Media
Page : 729 pages
File Size : 47,9 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9783322878694

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Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications by Josef Ballmann,Rolf Jeltsch Pdf

On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 55,9 Mb
Release : 1997-07-17
Category : Mathematics
ISBN : 3540629211

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Lectures on Nonlinear Hyperbolic Differential Equations by Lars Hörmander Pdf

In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.

Author : Song Jiang,Tatsien Li,Daqian Li
Publisher : World Scientific
Page : 793 pages
File Size : 47,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814417099

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Hyperbolic Problems by Song Jiang,Tatsien Li,Daqian Li Pdf

This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."

Author : Alain Haraux
Publisher : CRC Press
Page : 316 pages
File Size : 40,6 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 3718604604

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Semi-Linear Hyperbolic Problems in Bounded Domains by Alain Haraux Pdf

The opening chapter provides background information on the basic functional setting, semi-groups and the abstract wave equation, almost periodicity and the wave equation, and technical tools. Succeeding chapters cover the initial value problem, asymptotics in autonomous cases, non-resonance in the purely dissipative case, stability of periodic and almost-periodic solutions, oscillation properties in the conservative case, and global properties of the full equation. Includes bibliographic references and indexes by author and subject.

Author : Serge Alinhac
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461225782

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Blowup for Nonlinear Hyperbolic Equations by Serge Alinhac Pdf

Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as blowup. In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it.

Author : Randall J. LeVeque
Publisher : Cambridge University Press
Page : 582 pages
File Size : 42,6 Mb
Release : 2002-08-26
Category : Mathematics
ISBN : 0521009243

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Finite Volume Methods for Hyperbolic Problems by Randall J. LeVeque Pdf

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Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Publisher : Springer
Page : 446 pages
File Size : 50,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498049

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor Pdf

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Author : Heinrich Freistühler,Gerald Warnecke
Publisher : Birkhäuser
Page : 471 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883726

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Hyperbolic Problems: Theory, Numerics, Applications by Heinrich Freistühler,Gerald Warnecke Pdf

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Author : Sylvie Benzoni-Gavage,Denis Serre
Publisher : Springer Science & Business Media
Page : 1123 pages
File Size : 45,9 Mb
Release : 2008-01-12
Category : Mathematics
ISBN : 9783540757122

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Hyperbolic Problems: Theory, Numerics, Applications by Sylvie Benzoni-Gavage,Denis Serre Pdf

This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.