Lectures On Nonlinear Hyperbolic Differential Equations

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Lectures on Nonlinear Hyperbolic Differential Equations

Lars Hörmander

Author : Lars Hörmander
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 49,5 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.

Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor

Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Publisher : Springer
Page : 446 pages
File Size : 53,6 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.

Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Rainer Ansorge,Hester Bijl,Andreas Meister,Thomas Sonar

Author : Rainer Ansorge,Hester Bijl,Andreas Meister,Thomas Sonar
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 42,9 Mb
Release : 2012-09-14
Category : Technology & Engineering
ISBN : 9783642332203

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Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws by Rainer Ansorge,Hester Bijl,Andreas Meister,Thomas Sonar Pdf

In January 2012 an Oberwolfach workshop took place on the topic of recent developments in the numerics of partial differential equations. Focus was laid on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.

Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems

Michael Beals

Author : Michael Beals
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 44,5 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.

Lectures on Non-linear Wave Equations

Christopher Donald Sogge

Author : Christopher Donald Sogge
Publisher : Unknown
Page : 224 pages
File Size : 44,8 Mb
Release : 2008
Category : Nonlinear wave equations
ISBN : UCSD:31822035353036

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Lectures on Non-linear Wave Equations by Christopher Donald Sogge Pdf

Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.

Hyperbolic Partial Differential Equations

Peter D. Lax

Author : Peter D. Lax
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 55,5 Mb
Release : 2006
Category : Differential equations, Hyperbolic
ISBN : 9780821835760

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Hyperbolic Partial Differential Equations by Peter D. Lax Pdf

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Some Current Topics on Nonlinear Conservation Laws

Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics

Author : Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 40,9 Mb
Release : 2000
Category : Conservation laws (Mathematics).
ISBN : 9780821819654

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Some Current Topics on Nonlinear Conservation Laws by Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics Pdf

This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of $-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics. This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis. Titles in this series are co-published with International Press, Cambridge, MA.

Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1

Basil Nicolaenko,Darryl D. Holm,James M. Hyman

Author : Basil Nicolaenko,Darryl D. Holm,James M. Hyman
Publisher : American Mathematical Soc.
Page : 494 pages
File Size : 50,5 Mb
Release : 1986
Category : Mathematics
ISBN : 0821811258

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Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by Basil Nicolaenko,Darryl D. Holm,James M. Hyman Pdf

Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.

Lecture Notes on Numerical Methods for Hyperbolic Equations

Elena Vázquez-Cendón

Author : Elena Vázquez-Cendón
Publisher : CRC Press
Page : 144 pages
File Size : 44,6 Mb
Release : 2015-02-19
Category : Mathematics
ISBN : 1136618422

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Lecture Notes on Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón Pdf

This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro’s contribution to education and training on numerical methods for partial differential equations and was organized prior to the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications, which honours Professor Toro in the month of his 65th birthday. These lecture notes on selected topics in numerical methods for hyperbolic equations are from renowned academics in both theoretical and applied fields, and include contributions on: Nonlinear hyperbolic conservation laws First order schemes for the Euler equations High-order accuracy: monotonicity and non-linear methods High-order schemes for multidimensional hyperbolic problems A numerical method for the simulation of turbulent mixing and its basis in mathematical theory Lectures Notes on Numerical Methods for Hyperbolic Equations is intended primarily for research students and post-doctoral research fellows. Some background knowledge on the basics of the theoretical aspects of the partial differential equations, their physical meaning and discretization methods is assumed.

Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications

Josef Ballmann,Rolf Jeltsch

Author : Josef Ballmann,Rolf Jeltsch
Publisher : Springer Science & Business Media
Page : 729 pages
File Size : 44,8 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.

Nonlinear Partial Differential Equations in Geometry and Physics

Garth Baker,Alexandre S. Freire

Author : Garth Baker,Alexandre S. Freire
Publisher : Nelson Thornes
Page : 172 pages
File Size : 46,5 Mb
Release : 1997
Category : Mathematics
ISBN : 3764354933

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Nonlinear Partial Differential Equations in Geometry and Physics by Garth Baker,Alexandre S. Freire Pdf

This volume contains survey lectures in four different areas, delivered by leading researchers at the 1995 Barrett Lectures held at the University of Tennessee: nonlinear hyperbolic systems arising in field theory and relativity (S. Klainerman); harmonic maps from Minkowski spacetime (M. Struwe); dynamics of vortices in the Ginzburg-Landau model of superconductivity (F.-H. Lin); the Seiberg-Witten equations and their application to problems in four-dimensional topology (R. Fintushel). Most of this material has not previously been available in survey form. These lectures provide an up-to-date overview and an introduction to the research literature in each of these areas, which should prove useful to researchers and graduate students in mathematical physics, partial differential equations, differential geometry and topology.

Lectures on Differential Equations

Philip L. Korman

Author : Philip L. Korman
Publisher : American Mathematical Soc.
Page : 399 pages
File Size : 51,7 Mb
Release : 2019-08-30
Category : Differential equations
ISBN : 9781470451738

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Lectures on Differential Equations by Philip L. Korman Pdf

Lectures on Differential Equations provides a clear and concise presentation of differential equations for undergraduates and beginning graduate students. There is more than enough material here for a year-long course. In fact, the text developed from the author's notes for three courses: the undergraduate introduction to ordinary differential equations, the undergraduate course in Fourier analysis and partial differential equations, and a first graduate course in differential equations. The first four chapters cover the classical syllabus for the undergraduate ODE course leavened by a modern awareness of computing and qualitative methods. The next two chapters contain a well-developed exposition of linear and nonlinear systems with a similarly fresh approach. The final two chapters cover boundary value problems, Fourier analysis, and the elementary theory of PDEs. The author makes a concerted effort to use plain language and to always start from a simple example or application. The presentation should appeal to, and be readable by, students, especially students in engineering and science. Without being excessively theoretical, the book does address a number of unusual topics: Massera's theorem, Lyapunov's inequality, the isoperimetric inequality, numerical solutions of nonlinear boundary value problems, and more. There are also some new approaches to standard topics including a rethought presentation of series solutions and a nonstandard, but more intuitive, proof of the existence and uniqueness theorem. The collection of problems is especially rich and contains many very challenging exercises. Philip Korman is professor of mathematics at the University of Cincinnati. He is the author of over one hundred research articles in differential equations and the monograph Global Solution Curves for Semilinear Elliptic Equations. Korman has served on the editorial boards of Communications on Applied Nonlinear Analysis, Electronic Journal of Differential Equations, SIAM Review, an\ d Differential Equations and Applications.

Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations

Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze

Author : Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 444 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880732

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Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations by Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze Pdf

This volume focuses on recent developments in non-linear and hyperbolic equations. It will be a most valuable resource for researchers in applied mathematics, the theory of wavelets, and in mathematical and theoretical physics. Nine up-to-date contributions have been written on invitation by experts in the respective fields. The book is the third volume of the subseries "Advances in Partial Differential Equations".

Systems of Nonlinear Partial Differential Equations

J.M. Ball

Author : J.M. Ball
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400971899

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Systems of Nonlinear Partial Differential Equations by J.M. Ball Pdf

This volume contains the proceedings of a NATO/London Mathematical Society Advanced Study Institute held in Oxford from 25 July - 7 August 1982. The institute concerned the theory and applications of systems of nonlinear partial differential equations, with emphasis on techniques appropriate to systems of more than one equation. Most of the lecturers and participants were analysts specializing in partial differential equations, but also present were a number of numerical analysts, workers in mechanics, and other applied mathematicians. The organizing committee for the institute was J.M. Ball (Heriot-Watt), T.B. Benjamin (Oxford), J. Carr (Heriot-Watt), C.M. Dafermos (Brown), S. Hildebrandt (Bonn) and J.S. pym (Sheffield) . The programme of the institute consisted of a number of courses of expository lectures, together with special sessions on different topics. It is a pleasure to thank all the lecturers for the care they took in the preparation of their talks, and S.S. Antman, A.J. Chorin, J.K. Hale and J.E. Marsden for the organization of their special sessions. The institute was made possible by financial support from NATO, the London Mathematical Society, the u.S. Army Research Office, the u.S. Army European Research Office, and the u.S. National Science Foundation. The lectures were held in the Mathematical Institute of the University of Oxford, and residential accommodation was provided at Hertford College.

Lectures in Nonlinear Mechanics and Chaos Theory

Albert W Stetz

Author : Albert W Stetz
Publisher : World Scientific Publishing Company
Page : 140 pages
File Size : 54,8 Mb
Release : 2016-06-17
Category : Science
ISBN : 9789813141377

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Lectures in Nonlinear Mechanics and Chaos Theory by Albert W Stetz Pdf

This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be "solved" in the usual sense of the word. It then discusses perturbation theory which, rather than providing approximate solutions, fails catastrophically due to the problem of small denominators. It then goes on to describe chaotic motion using the tools of discrete maps and Poincaré sections. This leads to the two great landmarks of chaos theory, the Poincaré–Birkhoff theorem and the so-called KAM theorem, one of the signal results in modern mathematics. The book concludes with an appendix discussing the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics. Lectures on Nonlinear Mechanics and Chaos Theory is written in the easy conversational style of a great teacher. It features numerous computer-drawn figures illustrating the behavior of nonlinear systems. It also contains homework exercises and a selection of more detailed computational projects. The book will be valuable to students and faculty in physics, mathematics, and engineering. See Press Release: Problems in mechanics open the door to the orderly world of chaos

Lectures On Nonlinear Hyperbolic Differential Equations

Lectures on Nonlinear Hyperbolic Differential Equations by Lars Hörmander Pdf

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

Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws by Rainer Ansorge,Hester Bijl,Andreas Meister,Thomas Sonar Pdf

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

Lectures on Non-linear Wave Equations by Christopher Donald Sogge Pdf

Hyperbolic Partial Differential Equations by Peter D. Lax Pdf

Some Current Topics on Nonlinear Conservation Laws by Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics Pdf

Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by Basil Nicolaenko,Darryl D. Holm,James M. Hyman Pdf

Lecture Notes on Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón Pdf

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

Nonlinear Partial Differential Equations in Geometry and Physics by Garth Baker,Alexandre S. Freire Pdf

Lectures on Differential Equations by Philip L. Korman Pdf

Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations by Sergio Albeverio,Michael Demuth,Elmar Schrohe,Bert-Wolfgang Schulze Pdf

Systems of Nonlinear Partial Differential Equations by J.M. Ball Pdf

Lectures in Nonlinear Mechanics and Chaos Theory by Albert W Stetz Pdf

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