Well Posedness Of Linear Hyperbolic Problems

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Well-posedness of Linear Hyperbolic Problems

Author : Aleksandr Mikhaĭlovich Blokhin
Publisher : Nova Publishers
ISBN 13 : 9781594549762
Total Pages : 178 pages
Book Rating : 4.5/5 (497 download)

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Book Synopsis Well-posedness of Linear Hyperbolic Problems by : Aleksandr Mikhaĭlovich Blokhin

Download or read book Well-posedness of Linear Hyperbolic Problems written by Aleksandr Mikhaĭlovich Blokhin and published by Nova Publishers. This book was released on 2006 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book will be useful for students and specialists of partial differential equations and the mathematical sciences because it clarifies crucial points of Kreiss' symmetrizer technique. The Kreiss technique was developed by H.O. Kreiss for initial boundary value problems for linear hyperbolic systems. This technique is important because it involves equations that are used in many of the applied sciences. The research presented in this book takes unique approaches to exploring the Kreiss technique that will add insight and new perspectives to linear hyperbolic problems"--Publ. web site.

Hyperbolic Systems with Analytic Coefficients

Author : Tatsuo Nishitani
Publisher : Springer
ISBN 13 : 3319022733
Total Pages : 245 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Hyperbolic Systems with Analytic Coefficients by : Tatsuo Nishitani

Download or read book Hyperbolic Systems with Analytic Coefficients written by Tatsuo Nishitani and published by Springer. This book was released on 2013-11-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contain strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby.

New Trends in the Theory of Hyperbolic Equations

Author : Michael Reissig
Publisher : Springer Science & Business Media
ISBN 13 : 3764373865
Total Pages : 520 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis New Trends in the Theory of Hyperbolic Equations by : Michael Reissig

Download or read book New Trends in the Theory of Hyperbolic Equations written by Michael Reissig and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.

Semi-Linear Hyperbolic Problems in Bounded Domains

Author : Alain Haraux
Publisher : CRC Press
ISBN 13 : 9783718604609
Total Pages : 316 pages
Book Rating : 4.6/5 (46 download)

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Book Synopsis Semi-Linear Hyperbolic Problems in Bounded Domains by : Alain Haraux

Download or read book Semi-Linear Hyperbolic Problems in Bounded Domains written by Alain Haraux and published by CRC Press. This book was released on 1987-01-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The opening chapter provides background information on the basic functional setting, semi-groups and the abstract wave equation, almost periodicity and the wave equation, and technical tools. Succeeding chapters cover the initial value problem, asymptotics in autonomous cases, non-resonance in the purely dissipative case, stability of periodic and almost-periodic solutions, oscillation properties in the conservative case, and global properties of the full equation. Includes bibliographic references and indexes by author and subject.

Hyperbolic Problems: Theory, Numerics, Applications. Volume I

Author : Carlos Parés
Publisher : Springer Nature
ISBN 13 : 3031552601
Total Pages : 376 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications. Volume I by : Carlos Parés

Download or read book Hyperbolic Problems: Theory, Numerics, Applications. Volume I written by Carlos Parés and published by Springer Nature. This book was released on with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperbolic Equations and Related Topics

Author : Sigeru Mizohata
Publisher : Academic Press
ISBN 13 : 1483269256
Total Pages : 458 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Hyperbolic Equations and Related Topics by : Sigeru Mizohata

Download or read book Hyperbolic Equations and Related Topics written by Sigeru Mizohata and published by Academic Press. This book was released on 2014-05-10 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.

Hyperbolic Problems: Theory, Numerics, Applications

Author : Sylvie Benzoni-Gavage
Publisher : Springer Science & Business Media
ISBN 13 : 3540757120
Total Pages : 1117 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Sylvie Benzoni-Gavage

Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Sylvie Benzoni-Gavage and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 1117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modeling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly.

Multi-dimensional hyperbolic partial differential equations

Author : Sylvie Benzoni-Gavage
Publisher : OUP Oxford
ISBN 13 : 0191514187
Total Pages : 536 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Multi-dimensional hyperbolic partial differential equations by : Sylvie Benzoni-Gavage

Download or read book Multi-dimensional hyperbolic partial differential equations written by Sylvie Benzoni-Gavage and published by OUP Oxford. This book was released on 2006-11-23 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids. With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Hyperbolic Problems: Theory, Numerics and Applications

Author : Eitan Tadmor
Publisher : American Mathematical Soc.
ISBN 13 : 0821847295
Total Pages : 361 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics and Applications by : Eitan Tadmor

Download or read book Hyperbolic Problems: Theory, Numerics and Applications written by Eitan Tadmor and published by American Mathematical Soc.. This book was released on 2009 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.

Stiff Well Posedness for Hyperbolic Systems with Large Relaxation Terms

Author : Jenz Lorenz
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (756 download)

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Book Synopsis Stiff Well Posedness for Hyperbolic Systems with Large Relaxation Terms by : Jenz Lorenz

Download or read book Stiff Well Posedness for Hyperbolic Systems with Large Relaxation Terms written by Jenz Lorenz and published by . This book was released on 1996 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperbolic Partial Differential Equations

Author : Serge Alinhac
Publisher : Springer Science & Business Media
ISBN 13 : 0387878238
Total Pages : 159 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Hyperbolic Partial Differential Equations by : Serge Alinhac

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.

Hyperbolic Problems: Theory, Numerics, Applications

Author : Michael Fey
Publisher : Springer Science & Business Media
ISBN 13 : 9783764360870
Total Pages : 534 pages
Book Rating : 4.3/5 (68 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 Springer Science & Business Media. This book was released on 1999-04-01 with total page 534 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.

Hyperbolic Differential Operators And Related Problems

Author : Vincenzo Ancona
Publisher : CRC Press
ISBN 13 : 9780203911143
Total Pages : 390 pages
Book Rating : 4.9/5 (111 download)

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Book Synopsis Hyperbolic Differential Operators And Related Problems by : Vincenzo Ancona

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.

Well-Posedness of Parabolic Difference Equations

Author : A. Ashyralyev
Publisher : Birkhäuser
ISBN 13 : 3034885180
Total Pages : 367 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Well-Posedness of Parabolic Difference Equations by : A. Ashyralyev

Download or read book Well-Posedness of Parabolic Difference Equations written by A. Ashyralyev and published by Birkhäuser. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

Improperly Posed Problems in Partial Differential Equations

Author : L. E. Payne
Publisher : SIAM
ISBN 13 : 0898710197
Total Pages : 81 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Improperly Posed Problems in Partial Differential Equations by : L. E. Payne

Download or read book Improperly Posed Problems in Partial Differential Equations written by L. E. Payne and published by SIAM. This book was released on 1975-06-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of improperly posed Cauchy problems in partial differential equations

Hyperbolic Problems: Theory, Numerics, Applications

Author : Heinrich Freistühler
Publisher : Birkhäuser
ISBN 13 : 3034883722
Total Pages : 471 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Heinrich Freistühler

Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Heinrich Freistühler and published by Birkhäuser. This book was released on 2012-12-06 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has recently made considerable progress. Accurate and efficient numerical schemes for computation have been and are being further developed. This two-volume set of conference proceedings contains about 100 refereed and carefully selected papers. The books are intended for researchers and graduate students in mathematics, science and engineering interested in the most recent results in theory and practice of hyperbolic problems. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended thermodynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability of shock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite element schemes, adaptive, multiresolution, and artificial dissipation methods.

Hyperbolic Problems and Regularity Questions

Author : Mariarosaria Padula
Publisher : Springer Science & Business Media
ISBN 13 : 3764374519
Total Pages : 229 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Hyperbolic Problems and Regularity Questions by : Mariarosaria Padula

Download or read book Hyperbolic Problems and Regularity Questions written by Mariarosaria Padula and published by Springer Science & Business Media. This book was released on 2007-01-21 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.