Propagation of multidimensional nonlinear waves and kinematical conservation laws. (2018)

• Record Type: Book
• Further Information: Note: Phoolan Prasad.
• Authors: Prasad, Phoolan
• Contents: Intro; Preface; Contents; About the Author; 1 Introduction; 2 Scalar First-Order PDE; 2.1 Quasilinear PDE; 2.2 Examples and Some General Results; 2.3 Nonlinear Equation; 2.4 Example: Eikonal Equation; 3 Scalar Conservation Law; 3.1 Conservation Law and Curves of Discontinuity; 3.2 Stability Consideration, Entropy Condition and Shocks; 3.3 Riemann Problem; 3.4 Examples; 3.5 Nonlinear Wavefront and Shock Front; 4 Hyperbolic System of PDEs and Conservation Laws; 4.1 Ray Equations in a General System in d-D Space; 4.1.1 Wavefront Construction with the Help of Rays 4.2 Hyperbolic System of First-Order PDE4.2.1 Hyperbolic System in One Space Variable; 4.2.2 Simple Wave in One Space Dimension; 4.3 Hyperbolic System in Multi-dimensions; 4.3.1 The Wave Equation in d(>1) Space Dimensions; 4.3.2 Hyperbolic System in Multi-dimensions; 4.3.3 Characteristic Surface, Bicharacteristics and Rays; 4.4 Shocks, Jump Relations and Shock Manifold PDE; 4.4.1 One-Dimensinal System of Conservation Laws; 4.4.2 Multi-dimensional Systems of Conservation Laws; 5 Equations of Nonlinear Wavefront and Shock Front; 5.1 Weakly Nonlinear Ray Theory -- WNLRT 5.2 Shock Ray Theory (SRT) -- an Example in One Space Dimension5.3 SRT for a Shock in Multi-dimensions; 5.3.1 A Theorem on Shock Ray Equations for a Weak Shock; 5.3.2 SRT in a Polytropic Gas from WNLRT; 5.4 Non-dimensional Form of Equations of WNRT and SRT; 6 Kinematical Conservation Laws (KCL); 6.1 d-Dimensional KCL; 6.2 Equivalence of KCL and Ray Equations; 6.3 Kink Phenomenon; 7 Conservation Forms of Energy Transport Equations; 7.1 Ray Tube Area; 7.2 Energy Transport Equation in 3-D WNLRT; 7.3 Transport Equations in 3-D SRT; 7.4 Energy Transport Equations in 2-D 9.2 Nonlinear Wavefront Produced by a Convex Piston9.3 Evolution of a Shock Front of Periodic Shape; 9.4 Corrugational Stability; 9.5 Evolution of a Shock from Closed Curves into Circles; 9.6 Sonic Boom by a Maneuvering Aerofoil; 9.6.1 Description and Basic Assumptions; 9.6.2 Introduction of a Ray Coordinate System; 9.6.3 Cauchy Data in Ray Coordinates; 9.6.4 Results; 10 3-D WNLRT and SRT: Theory and Applications; 10.1 Eigen Structure of the WNLRT Equations; 10.2 Eigen Structure of the SRT Equations; 10.3 Numerical Approximation of the SRT Equations
• Publisher Details: Singapore : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 531/.1133; Mathematics; Nonlinear wave equations; Kinematics; SCIENCE / Mechanics / General; SCIENCE / Mechanics / Solids; Kinematics; Nonlinear wave equations; Mathematics -- Applied; Mathematics -- Differential Equations; Mathematical modelling; Differential calculus & equations; Differential equations, partial; Differential Equations; Electronic books
• Languages: English
• ISBNs: 9789811075810; 9811075816
• Related ISBNs: 9789811075803; 9811075808
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed March 14, 2018)
• 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.