Nonlinear Hyperbolic Waves In Multidimensions

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Nonlinear Hyperbolic Waves in Multidimensions

Phoolan Prasad
Nonlinear Hyperbolic Waves in Multidimensions Book PDF

Author : Phoolan Prasad
Publisher : Chapman and Hall/CRC
Page : 360 pages
File Size : 52,7 Mb
Release : 2001-05-18
Category : Mathematics
ISBN : 1584880724

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Nonlinear Hyperbolic Waves in Multidimensions by Phoolan Prasad Pdf

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts. Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts in gas dynamics, a graphical presentation of the results of extensive numerical computations, and an extension of Fermat's principle. There is also a chapter containing approximate equations used to discuss stability of steady transonic flows. Full of new and original results, Nonlinear Hyperbolic Waves in Multidimensions is your only opportunity to explore a full treatment of these recent findings in book form. The material presented in this volume will prove useful not only for solving practical problems, but also in raising many difficult but important mathematical questions that remain open.

Nonlinear Hyperbolic Waves in Multi-Dimensions

Phoolan Prasad
Nonlinear Hyperbolic Waves in Multi Dimensions Book PDF

Author : Phoolan Prasad
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 1999-05
Category : Electronic
ISBN : 0582322650

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Nonlinear Hyperbolic Waves in Multi-Dimensions by Phoolan Prasad Pdf

The propagation of curved, nonlinear wavefronts and shock fronts is a very complex phenomena. This book provides a self-contained account an d gradual development of mathematical methods for studying successive positions of these fronts. It includes an introduction to shock fronts, derives the ray theory for a nonlinear wavefront, discusses kink phe nomena, develops a new theory for plane and curved shock propagation, and contains Huygens' method of wavefronts construction and an extensi on of Fermat's principle. The book also has approximate equations to d iscuss stability of steady transonic flows. The author includes a num ber of examples of the theory to converging wavefronts in gasdynamics and demonstrates numerical computations. All of the results presented are new and were developed by the author and his research group.

Nonlinear Hyperbolic Waves in Multidimensions

Phoolan Prasad
Nonlinear Hyperbolic Waves in Multidimensions Book PDF

Author : Phoolan Prasad
Publisher : CRC Press
Page : 360 pages
File Size : 43,6 Mb
Release : 2001-05-18
Category : Mathematics
ISBN : 9781420026146

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Nonlinear Hyperbolic Waves in Multidimensions by Phoolan Prasad Pdf

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts. Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts in gas dynamics, a graphical presentation of the results of extensive numerical computations, and an extension of Fermat's principle. There is also a chapter containing approximate equations used to discuss stability of steady transonic flows. Full of new and original results, Nonlinear Hyperbolic Waves in Multidimensions is your only opportunity to explore a full treatment of these recent findings in book form. The material presented in this volume will prove useful not only for solving practical problems, but also in raising many difficult but important mathematical questions that remain open.

Global Propagation of Regular Nonlinear Hyperbolic Waves

Tatsien Li,Wang Libin
Global Propagation of Regular Nonlinear Hyperbolic Waves Book PDF

Author : Tatsien Li,Wang Libin
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 44,7 Mb
Release : 2009-09-01
Category : Science
ISBN : 9780817646356

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Global Propagation of Regular Nonlinear Hyperbolic Waves by Tatsien Li,Wang Libin Pdf

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.

Global Propagation of Regular Nonlinear Hyperbolic Waves

Tatsien Li,Wang Libin
Global Propagation of Regular Nonlinear Hyperbolic Waves Book PDF

Author : Tatsien Li,Wang Libin
Publisher : Birkhäuser
Page : 252 pages
File Size : 52,9 Mb
Release : 2011-11-02
Category : Science
ISBN : 0817671684

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Global Propagation of Regular Nonlinear Hyperbolic Waves by Tatsien Li,Wang Libin Pdf

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.

Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws

Phoolan Prasad
Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws Book PDF

Author : Phoolan Prasad
Publisher : Springer
Page : 159 pages
File Size : 46,8 Mb
Release : 2018-03-06
Category : Mathematics
ISBN : 9789811075810

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Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws by Phoolan Prasad Pdf

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.

Multidimensional Hyperbolic Problems and Computations

James Glimm,Andrew J. Majda
Multidimensional Hyperbolic Problems and Computations Book PDF

Author : James Glimm,Andrew J. Majda
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461391210

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Multidimensional Hyperbolic Problems and Computations by James Glimm,Andrew J. Majda Pdf

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

Linear and Nonlinear Waves

G. B. Whitham
Linear and Nonlinear Waves Book PDF

Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 44,7 Mb
Release : 2011-10-18
Category : Science
ISBN : 9781118031209

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Linear and Nonlinear Waves by G. B. Whitham Pdf

Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Wind Over Waves

S G Sajjadi,J C R Hunt
Wind Over Waves Book PDF

Author : S G Sajjadi,J C R Hunt
Publisher : Elsevier
Page : 250 pages
File Size : 53,8 Mb
Release : 2003-07-01
Category : Science
ISBN : 9780857099532

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Wind Over Waves by S G Sajjadi,J C R Hunt Pdf

This book addresses ocean wave processes and turbulence as they affect oceanography, meteorology, marine and coastal engineering. It will enable applied mathematicians, seafarers, and all others affected by these phenomena to predict and control wave effects on shipping safety, weather forecasting, offshore structures, sediment pollution, and ice dynamics in polar regions. The focus is on analytical and computational methods for solving equations of motion and studying non-linear aspects of waves and turbulence. Results included show how sudden gusts and winds over waves can modify the mechanisms of wave-breaking and oceanic turbulence. The book records the proceedings of the Wind Over Waves conference of the Institute of Mathematics and its Applications at Churchill College, Cambridge. Co-sponsors with the IMA are the Institute of Civil Engineers and the Royal Meteorological Society. Addresses ocean wave processes and turbulence as they affect oceanography, meteorology, marine and coastal engineering Focuses on analytical and computational methods for solving equations of motion and studying non-linear aspects of waves and turbulence Records the proceedings of the Wind Over Waves conference of the Institute of Mathematics and its Applications at Churchill College, Cambridge

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena Book PDF

Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 53,9 Mb
Release : 2010-10-01
Category : Mathematics
ISBN : 9780821849767

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Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations Pdf

This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

Nonlinear Wave Equations

Satyanad Kichenassamy
Nonlinear Wave Equations Book PDF

Author : Satyanad Kichenassamy
Publisher : CRC Press
Page : 297 pages
File Size : 47,7 Mb
Release : 2021-05-30
Category : Mathematics
ISBN : 9781000444728

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Nonlinear Wave Equations by Satyanad Kichenassamy Pdf

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.

Analytical Approaches to Multidimensional Balance Laws

Olga S. Rozanova
Analytical Approaches to Multidimensional Balance Laws Book PDF

Author : Olga S. Rozanova
Publisher : Nova Publishers
Page : 260 pages
File Size : 48,5 Mb
Release : 2006
Category : Science
ISBN : 1594543070

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Analytical Approaches to Multidimensional Balance Laws by Olga S. Rozanova Pdf

It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.

Nonlinear Wave Equations

Walter A. Strauss
Nonlinear Wave Equations Book PDF

Author : Walter A. Strauss
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 41,9 Mb
Release : 1990-01-12
Category : Mathematics
ISBN : 9780821807255

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Nonlinear Wave Equations by Walter A. Strauss Pdf

The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

Handbook of Differential Equations: Evolutionary Equations

C.M. Dafermos,Eduard Feireisl
Handbook of Differential Equations Evolutionary Equations Book PDF

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 676 pages
File Size : 44,5 Mb
Release : 2005-10-05
Category : Mathematics
ISBN : 0080461387

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Hyperbolic Problems: Theory, Numerics, Applications

Michael Fey,Rolf Jeltsch
Hyperbolic Problems Theory Numerics Applications Book PDF

Author : Michael Fey,Rolf Jeltsch
Publisher : Birkhäuser
Page : 514 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887243

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Hyperbolic Problems: Theory, Numerics, Applications by Michael Fey,Rolf Jeltsch Pdf

[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.