| Document Type
|
:
|
BL
|
| Record Number
|
:
|
889144
|
| Main Entry
|
:
|
Prasad, Phoolan
|
| Title & Author
|
:
|
Propagation of multidimensional nonlinear waves and kinematical conservation laws /\ Phoolan Prasad.
|
| Publication Statement
|
:
|
Singapore :: Springer,, 2018.
|
| Series Statement
|
:
|
Infosys Science Foundation series, Infosys Science Foundation series in mathematical sciences,
|
| Page. NO
|
:
|
1 online resource
|
| ISBN
|
:
|
9789811075810
|
|
|
:
|
: 9811075816
|
|
|
:
|
9789811075803
|
|
|
:
|
9811075808
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and index.
|
| 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
|
| Subject
|
:
|
Kinematics.
|
| Subject
|
:
|
Nonlinear wave equations.
|
| Subject
|
:
|
Differential calculus equations.
|
| Subject
|
:
|
Kinematics.
|
| Subject
|
:
|
Mathematical modelling.
|
| Subject
|
:
|
Nonlinear wave equations.
|
| Subject
|
:
|
SCIENCE-- Mechanics-- General.
|
| Subject
|
:
|
SCIENCE-- Mechanics-- Solids.
|
| Dewey Classification
|
:
|
531/.1133
|
| LC Classification
|
:
|
QC174.26.W28
|