Nonlinear hyperbolic waves in multi-dimensions. (©2001)

• Record Type: Book
• Further Information: Note: Phoolan Prasad.
• Other Names: Prasad, Phoolan
• 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, 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 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
• Publisher Details: Boca Raton, Fla : Chapman & Hall/CRC
• Publication Date: 2001
• Copyright Date: 2001
• Extent: 1 online resource (xvi, 338 pages), illustrations
• Subjects: 531/.1133/01515355; Nonlinear wave equations; Differential equations, Hyperbolic; Équations d'onde non linéaires; Équations différentielles hyperboliques; SCIENCE -- Waves & Wave Mechanics; Differential equations, Hyperbolic; Nonlinear wave equations; Electronic books
• Languages: English
• ISBNs: 1420026143; 9781420026146; 9781584880721; 1584880724
• Related ISBNs: 1584880724
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.