Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems
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Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems
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Author : Michael Beals
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Propagation And Interaction Of Singularities In Nonlinear Hyperbolic Problems written by Michael Beals and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Nonlinear Hyperbolic Equations And Field Theory
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Author : M K V Murthy
language : en
Publisher: CRC Press
Release Date : 1992-03-30
Nonlinear Hyperbolic Equations And Field Theory written by M K V Murthy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-30 with Mathematics categories.
Contains the proceedings of a workshop on nonlinear hyperbolic equations held at Varenna, Italy in June 1990.
Analysis Of Singularities For Partial Differential Equations
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Author : Shuxing Chen
language : en
Publisher: World Scientific
Release Date : 2010-09-24
Analysis Of Singularities For Partial Differential Equations written by Shuxing Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-24 with Mathematics categories.
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.
Symbolic Calculus Semilinear Hyperbolic Progressing Waves
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Author : Hassane Bougrini
language : en
Publisher: Nova Publishers
Release Date : 2000
Symbolic Calculus Semilinear Hyperbolic Progressing Waves written by Hassane Bougrini and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main purpose of this book is to give a self-contained synthesis of different results in the domain of symbolic calculus of conormal singularities of semilinear hyperbolic progressing waves. The authors deal generally with real matrix valued co-efficients and with real vector valued solutions, but the complex case is similar. They consider also N x N first order systems rather than high order scalar equations, because the polarisation properties of symbols are less natural in the latter case. Moreover, although they assume generally that the real characteristics are simple, the methods can give results for symmetric or symmetrisable first order hyperbolic systems.
Nonlinear Wave Equations
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Author : Satyanad Kichenassamy
language : en
Publisher: CRC Press
Release Date : 2021-05-30
Nonlinear Wave Equations written by Satyanad Kichenassamy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-30 with Mathematics categories.
This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Proceedings Of The Third Asian Mathematical Conference 2000
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Author : Toshikazu Sunada
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The Third Asian Mathematical Conference 2000 written by Toshikazu Sunada and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
COntains 55 research and expository articles on a wide range of currently active and interesting areas in pure and applied mathematics.
Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Author : Tatsien Li
language : en
Publisher: Birkhäuser
Release Date : 2011-11-02
Global Propagation Of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-02 with Science categories.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Partial Differential Equations Iii
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Author : Michael Taylor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Partial Differential Equations Iii written by Michael Taylor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis. ^
Nonlinear Functional Analysis And Its Applications
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Author : E. Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Nonlinear Functional Analysis And Its Applications written by E. Zeidler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
Pseudodifferential Operators And Nonlinear Pde
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Author : Michael Taylor
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-01
Pseudodifferential Operators And Nonlinear Pde written by Michael Taylor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-01 with Mathematics categories.
For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis.