Nonlinear Hyperbolic Waves In Multidimensions

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Nonlinear Hyperbolic Waves in Multidimensions

Author : Phoolan Prasad
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781584880721
Total Pages : 360 pages
Book Rating : 4.8/5 (87 download)

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Book Synopsis Nonlinear Hyperbolic Waves in Multidimensions by : Phoolan Prasad

Download or read book Nonlinear Hyperbolic Waves in Multidimensions written by Phoolan Prasad and published by Chapman and Hall/CRC. This book was released on 2001-05-18 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Phoolan Prasad
Publisher :
ISBN 13 : 9780582322653
Total Pages : pages
Book Rating : 4.3/5 (226 download)

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Book Synopsis Nonlinear Hyperbolic Waves in Multi-Dimensions by : Phoolan Prasad

Download or read book Nonlinear Hyperbolic Waves in Multi-Dimensions written by Phoolan Prasad and published by . This book was released on 1999-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Phoolan Prasad
Publisher : CRC Press
ISBN 13 : 1420026143
Total Pages : 360 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Nonlinear Hyperbolic Waves in Multidimensions by : Phoolan Prasad

Download or read book Nonlinear Hyperbolic Waves in Multidimensions written by Phoolan Prasad and published by CRC Press. This book was released on 2001-05-18 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Tatsien Li
Publisher : Springer Science & Business Media
ISBN 13 : 0817646353
Total Pages : 252 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Global Propagation of Regular Nonlinear Hyperbolic Waves by : Tatsien Li

Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Phoolan Prasad
Publisher : Springer
ISBN 13 : 9811075816
Total Pages : 159 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws by : Phoolan Prasad

Download or read book Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws written by Phoolan Prasad and published by Springer. This book was released on 2018-03-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Propagation of Regular Nonlinear Hyperbolic Waves

Author : Tatsien Li
Publisher : Birkhäuser
ISBN 13 : 9780817671686
Total Pages : 252 pages
Book Rating : 4.6/5 (716 download)

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Book Synopsis Global Propagation of Regular Nonlinear Hyperbolic Waves by : Tatsien Li

Download or read book Global Propagation of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and published by Birkhäuser. This book was released on 2011-11-02 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multidimensional Hyperbolic Problems and Computations

Author : James Glimm
Publisher : Springer Science & Business Media
ISBN 13 : 1461391210
Total Pages : 399 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multidimensional Hyperbolic Problems and Computations by : James Glimm

Download or read book Multidimensional Hyperbolic Problems and Computations written by James Glimm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : G. B. Whitham
Publisher : John Wiley & Sons
ISBN 13 : 1118031202
Total Pages : 660 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Linear and Nonlinear Waves by : G. B. Whitham

Download or read book Linear and Nonlinear Waves written by G. B. Whitham and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher : American Mathematical Soc.
ISBN 13 : 082184976X
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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

Download or read book Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations and published by American Mathematical Soc.. This book was released on 2010-10-01 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Wind Over Waves

Author : S G Sajjadi
Publisher : Elsevier
ISBN 13 : 0857099531
Total Pages : 250 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Wind Over Waves by : S G Sajjadi

Download or read book Wind Over Waves written by S G Sajjadi and published by Elsevier. This book was released on 2003-07-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Analytical Approaches to Multidimensional Balance Laws

Author : Olga S. Rozanova
Publisher : Nova Publishers
ISBN 13 : 9781594543074
Total Pages : 260 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Analytical Approaches to Multidimensional Balance Laws by : Olga S. Rozanova

Download or read book Analytical Approaches to Multidimensional Balance Laws written by Olga S. Rozanova and published by Nova Publishers. This book was released on 2006 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 9780080461380
Total Pages : 676 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2005-10-05 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Singularities and Oscillations

Author : Jeffrey Rauch
Publisher : Springer Science & Business Media
ISBN 13 : 1461219728
Total Pages : 161 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Singularities and Oscillations by : Jeffrey Rauch

Download or read book Singularities and Oscillations written by Jeffrey Rauch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary, to the examination of viscous boundary layers. It examines the foundations of the theory of high- frequency electromagnetic waves in a dielectric or semiconducting medium. Nor are unifying themes entirely absent from nonlinear analysis: one chapter considers microlocal analysis, including paradifferential operator calculus, on Morrey spaces, and connections with various classes of partial differential equations.

Hyperbolic Problems: Theory, Numerics, Applications

Author : Michael Fey
Publisher : Birkhäuser
ISBN 13 : 3034887248
Total Pages : 514 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Michael Fey

Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Michael Fey and published by Birkhäuser. This book was released on 2012-12-06 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: [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.

Analysis and Numerics for Conservation Laws

Author : Gerald Warnecke
Publisher : Springer Science & Business Media
ISBN 13 : 3540279075
Total Pages : 542 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Analysis and Numerics for Conservation Laws by : Gerald Warnecke

Download or read book Analysis and Numerics for Conservation Laws written by Gerald Warnecke and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.

Nonlinear Wave Equations

Author : Satyanad Kichenassamy
Publisher : CRC Press
ISBN 13 : 1000444724
Total Pages : 297 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Large Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems

Author : Guy Métivier
Publisher : American Mathematical Soc.
ISBN 13 : 0821836498
Total Pages : 107 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Large Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems by : Guy Métivier

Download or read book Large Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems written by Guy Métivier and published by American Mathematical Soc.. This book was released on 2005 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error. The rate of convergence for this approximation is obtained. The integral transformations are combined with the idea of probability structure preserving mapping introduced in [48] and are applied to develop a stochastic calculus for fractional Brownian motions of all Hurst parameter $H\in (0, 1)$. In particular we obtain Radon-Nikodym derivative of nonlinear (random) translation of fractional Brownian motion over finite interval, extending the results of [48] to general case. We obtain an integration by parts formula for general stochastic integral and an Ito type formula for some stochastic integral.The conditioning, Clark derivative, continuity of stochastic integral are also studied. As an application we study a linear quadratic control problem, where the system is driven by fractional Brownian motion.