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mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonlinear hyperbolic waves in multi-dimensions
  name:
    name part: Prasad, Phoolan.
    role:
      role term: creator
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    place:
      place term: Boca Raton, Fla
    publisher: Chapman & Hall/CRC
    date issued: ©2001
    date issued: 2001
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xvi, 338 pages) : illustrations.
  abstract: Annotation 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.
  table of contents: AN INTRODUCTION TO NONLINEAR HYPERBOLIC WAVES; A Wave Equation with Genuine Nonlinearity; Breakdown of a Genuine Solution; Conservation Law and Jump Condition; Stability Consideration, Entropy Condition, and Shocks; Some Examples; Shock Structure, Dissipation and Entropy Condition; The Persistence of a Shock; Nonlinear Wavefront and Shock Front; Hopf's Result on the General Solution; Equal Area Rule for Shock Fitting; HYPERBOLIC SYSTEM-SOME BASIC RESULTS; Hyperbolic System of First Order Equations in Two Independent Variables; The Wave Equation in m(>1) Space Dimensions; Hyperbolic System in More than Two Independent Variables; Bicharacteristic Curves, Rays, and Compatibility Condition; Propagation of Discontinuities of First Order Derivatives Along Rays; SIMPLE WAVE, HIGH FREQUENCY APPROXIMATION, AND RAY THEORY; Simple Wave; High-Frequency Approximation, Wavefront,
  table of contents: Huygens' Method and Fermat's Principle; Kinematics of a Propagating Curve; Breakdown of the Continuity of a Solution of a Quasilinear System; Jump Conditions for a Curved Shock; WEAKLY NONLINEAR RAY THEORY (WNLRT) DERIVATION; A Historical Account; Derivation of CPW Theory; A Geometric Derivation of WNLRT; An Asymptotic Derivation of WNLRT; STABILITY OF SOLUTIONS NEAR A SINGULARITY OF SONIC TYPE; Introduction; One-Dimensional Weakly Nonlinear Wave Propagation; Waves in a Multi-Dimensional Steady Transonic Flow; WNLRT IN A POLYTROPIC GAS; Basic Equations; Geometrical Features of a Nonlinear Wavefront; Exact Solution of an Initial Value Problem; Conclusion and Validity of WNLRT; COMPATIBILITY CONDITIONS ON A SHOCK: SINGLE CONSERVATION LAW; Derivation of the Infinite System of Compatibility Conditions; Existence and Uniqueness of the Solution of the Infinite System; A New Theory of Shock Dynamics: Analytic Considerations; A New Theory of Shock.
  table of contents: Dynamics: Comparison of Numerical Results with the Exact Solution; Conclusion; ONE-DIMENSIONAL PISTON PROBLEM: AN APPLICATION OF NTSD; Formulation of the Problem; Dynamical Compatibility Conditions; Initial Conditions for the Piston Problem; Results and Discussions; COMPATIBILITY CONDITIONS ON A MULTI-DIMENSIONAL SHOCK; Shock Rays; Shock Manifold Equation for a Weak Shock; Geometrical and Kinematical Compatibility Conditions; Dynamical Compatibility Conditions; A Weak Shock Ray Theory; PROPAGATION OF A CURVED WEAK SHOCK; Governing Equations of the NTSD; Conservation Form of the Equations for a 2-Dimensional Shock Propagation; Initial Conditions, Results, and Discussion; Comparison with other Theories; Corrugational Stability and Persistence of a Kink.
  note: Phoolan Prasad.
  note: Includes bibliographical references and index.
  subject:
    topic: Nonlinear wave equations
  subject:
    topic: Differential equations, Hyperbolic
  subject:
    topic: Équations d'onde non linéaires
  subject:
    topic: Équations différentielles hyperboliques
  subject:
    topic: SCIENCE
    topic: Waves & Wave Mechanics
  subject:
    topic: Differential equations, Hyperbolic
  subject:
    topic: Nonlinear wave equations
  classification: QA927 .P73 2001eb
  classification: 531/.1133/01515355
  related item:
    title info:
      title: Nonlinear hyperbolic waves in multi-dimensions
    name:
      name part: Prasad, Phoolan.
    origin info:
      publisher: Boca Raton, Fla. : Chapman & Hall/CRC, ©2001
    identifier: (DLC) 2001017331
    identifier: (OCoLC)45861957
  related item:
    title info:
      title: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 121
  identifier: 1420026143
  identifier: 9781420026146
  identifier: 9781584880721
  identifier: 1584880724
  identifier: TANDF_191976 Ingram Content Group
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 060822
    record change date: 20241111204555.6
    record identifier: in00005527027
    language of cataloging:
      language term: eng