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Author : Florent J. Bureau
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.3/5 (91 download)
Download or read book Research in Hyperbolic Differential Equations written by Florent J. Bureau and published by . This book was released on 1960 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Serge Alinhac
Publisher : Springer Science & Business Media
ISBN 13 : 0387878238
Total Pages : 159 pages
Book Rating : 4.3/5 (878 download)
Download or read book Hyperbolic Partial Differential Equations written by Serge Alinhac and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
Author : Peter D. Lax
Publisher : American Mathematical Soc.
ISBN 13 : 0821835769
Total Pages : 234 pages
Book Rating : 4.8/5 (218 download)
Download or read book Hyperbolic Partial Differential Equations written by Peter D. Lax and published by American Mathematical Soc.. This book was released on 2006 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Florent J. Bureau
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (227 download)
Download or read book Research in Hyperbolic Differential Equations written by Florent J. Bureau and published by . This book was released on 1970 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report contains conclusions of investigations on: (1) The Cauchy problem for partial differential equations of order n greater than 2 and p greater than 2 independent variables; (b) Boundary value problems for totally hyperbolic equations in several independent variables; (3) Problems suggested by and related to the above areas. (Author).
Author : Jeffrey Rauch
Publisher : American Mathematical Soc.
ISBN 13 : 0821872915
Total Pages : 386 pages
Book Rating : 4.8/5 (218 download)
Download or read book Hyperbolic Partial Differential Equations and Geometric Optics written by Jeffrey Rauch and published by American Mathematical Soc.. This book was released on 2012-05-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.
Author : Andreas Meister
Publisher : Springer Science & Business Media
ISBN 13 : 3322802272
Total Pages : 329 pages
Book Rating : 4.3/5 (228 download)
Download or read book Hyperbolic Partial Differential Equations written by Andreas Meister and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modelling of various problems from practice. It shows in an unique manner concepts for the numerical treatment of such equations starting from basic algorithms up actual research topics in this area. The numerical methods discussed are central and upwind schemes for structured and unstructured grids based on ENO and WENO reconstructions, pressure correction schemes like SIMPLE and PISO as well as asymptotic-induced algorithms for low-Mach number flows.
Author : Horst Reinhard Beyer
Publisher : Springer
ISBN 13 : 3540711295
Total Pages : 291 pages
Book Rating : 4.5/5 (47 download)
Download or read book Beyond Partial Differential Equations written by Horst Reinhard Beyer and published by Springer. This book was released on 2007-04-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.
Author : Lars Hörmander
Publisher : Springer Science & Business Media
ISBN 13 : 9783540629214
Total Pages : 308 pages
Book Rating : 4.6/5 (292 download)
Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 1997-07-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Mass Per Pettersson
Publisher : Springer
ISBN 13 : 3319107143
Total Pages : 214 pages
Book Rating : 4.3/5 (191 download)
Download or read book Polynomial Chaos Methods for Hyperbolic Partial Differential Equations written by Mass Per Pettersson and published by Springer. This book was released on 2015-03-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.
Author : Mitsuru Ikawa
Publisher : American Mathematical Soc.
ISBN 13 : 9780821810217
Total Pages : 218 pages
Book Rating : 4.8/5 (12 download)
Download or read book Hyperbolic Partial Differential Equations and Wave Phenomena written by Mitsuru Ikawa and published by American Mathematical Soc.. This book was released on 2000 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wave-like phenomena. The primary theme of this book is the mathematical investigation of such wave phenomena. The exposition begins with derivations of some wave equations, including waves in an elastic body, such as those observed in connection with earthquakes. Certain existence results are proved early on, allowing the later analysis to concentrate on properties of solutions. The existence of solutions is established using methods from functional analysis. Many of the properties are developed using methods of asymptotic solutions. The last chapter contains an analysis of the decay of the local energy of solutions. This analysis shows, in particular, that in a connected exterior domain, disturbances gradually drift into the distance and the effect of a disturbance in a bounded domain becomes small after sufficient time passes. The book is geared toward a wide audience interested in PDEs. Prerequisite to the text are some real analysis and elementary functional analysis. It would be suitable for use as a text in PDEs or mathematical physics at the advanced undergraduate and graduate level.
Author : Vincenzo Ancona
Publisher : CRC Press
ISBN 13 : 9780203911143
Total Pages : 390 pages
Book Rating : 4.9/5 (111 download)
Download or read book Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and published by CRC Press. This book was released on 2003-03-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Author : Sylvie Benzoni-Gavage
Publisher : Oxford University Press on Demand
ISBN 13 : 019921123X
Total Pages : 535 pages
Book Rating : 4.1/5 (992 download)
Download or read book Multi-dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and published by Oxford University Press on Demand. This book was released on 2007 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Author : Yurii Vladimirovich Egorov
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (112 download)
Download or read book Partial Differential Equations IV written by Yurii Vladimirovich Egorov and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.W. Thomas
Publisher : Springer Science & Business Media
ISBN 13 : 1489972781
Total Pages : 451 pages
Book Rating : 4.4/5 (899 download)
Download or read book Numerical Partial Differential Equations: Finite Difference Methods written by J.W. Thomas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
Author : Shi Jin
Publisher : Springer
ISBN 13 : 3319671103
Total Pages : 277 pages
Book Rating : 4.3/5 (196 download)
Download or read book Uncertainty Quantification for Hyperbolic and Kinetic Equations written by Shi Jin and published by Springer. This book was released on 2018-03-20 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.
Author : Saïd Abbas
Publisher : Springer Science & Business Media
ISBN 13 : 146144036X
Total Pages : 403 pages
Book Rating : 4.4/5 (614 download)
Download or read book Topics in Fractional Differential Equations written by Saïd Abbas and published by Springer Science & Business Media. This book was released on 2012-08-17 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists.
Author : G Geymonat
Publisher : World Scientific
ISBN 13 : 9814507857
Total Pages : 190 pages
Book Rating : 4.8/5 (145 download)
Download or read book Partial Differential Equations Of Hyperbolic Type And Applications written by G Geymonat and published by World Scientific. This book was released on 1987-02-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the general aspects of hyperbolic conservation laws and their numerical approximation using some of the most modern tools: spectral methods, unstructured meshes and λ-formulation. The applications of these methods are found in some significant examples such as the Euler equations. This book, a collection of articles by the best authors in the field, exposes the reader to the frontier of the research and many open problems.
