Buch, Englisch, 360 Seiten, Format (B × H): 163 mm x 240 mm, Gewicht: 679 g
Reihe: Monographs and Surveys in Pure and Applied Mathematics
Buch, Englisch, 360 Seiten, Format (B × H): 163 mm x 240 mm, Gewicht: 679 g
Reihe: Monographs and Surveys in Pure and Applied Mathematics
ISBN: 978-1-58488-072-1
Verlag: Chapman and Hall/CRC
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.
Zielgruppe
Applied mathematicians in nonlinear waves and gas dynamics, aeronautical engineers, and mechanical engineers
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
AN INTRODUCTION TO NONLINEAR HYPERBOLIC WAVESA Wave Equation with Genuine NonlinearityBreakdown of a Genuine SolutionConservation Law and Jump ConditionStability Consideration, Entropy Condition, and ShocksSome ExamplesShock Structure, Dissipation and Entropy ConditionThe Persistence of a ShockNonlinear Wavefront and Shock FrontHopf's Result on the General SolutionEqual Area Rule for Shock FittingHYPERBOLIC SYSTEM-SOME BASIC RESULTSHyperbolic System of First Order Equations in Two Independent VariablesThe Wave Equation in m(>1) Space DimensionsHyperbolic System in More than Two Independent VariablesBicharacteristic Curves, Rays, and Compatibility ConditionPropagation of Discontinuities of First Order Derivatives Along RaysSIMPLE WAVE, HIGH FREQUENCY APPROXIMATION, AND RAY THEORYSimple WaveHigh-Frequency Approximation, Wavefront, Huygens' Method and Fermat's PrincipleKinematics of a Propagating CurveBreakdown of the Continuity of a Solution of a Quasilinear SystemJump Conditions for a Curved ShockWEAKLY NONLINEAR RAY THEORY (WNLRT) DERIVATIONA Historical AccountDerivation of CPW TheoryA Geometric Derivation of WNLRTAn Asymptotic Derivation of WNLRTSTABILITY OF SOLUTIONS NEAR A SINGULARITY OF SONIC TYPEIntroductionOne-Dimensional Weakly Nonlinear Wave PropagationWaves in a Multi-Dimensional Steady Transonic FlowWNLRT IN A POLYTROPIC GASBasic EquationsGeometrical Features of a Nonlinear WavefrontExact Solution of an Initial Value ProblemConclusion and Validity of WNLRTCOMPATIBILITY CONDITIONS ON A SHOCK: SINGLE CONSERVATION LAWDerivation of the Infinite System of Compatibility ConditionsExistence and Uniqueness of the Solution of the Infinite SystemA New Theory of Shock Dynamics: Analytic ConsiderationsA New Theory of Shock Dynamics: Comparison of Numerical Results with the Exact SolutionConclusionONE-DIMENSIONAL PISTON PROBLEM: AN APPLICATION OF NTSDFormulation of the ProblemDynamical Compatibility ConditionsInitial Conditions for the Piston ProblemResults and Discussions COMPATIBILITY CONDITIONS ON A MULTI-DIMENSIONAL SHOCKShock RaysShock Manifold Equation for a Weak ShockGeometrical and Kinematical Compatibility ConditionsDynamical Compatibility ConditionsA Weak Shock Ray TheoryPROPAGATION OF A CURVED WEAK SHOCKGoverning Equations of the NTSDConservation Form of the Equations for a 2-Dimensional Shock PropagationInitial Conditions, Results, and DiscussionComparison with other TheoriesCorrugational Stability and Persistence of a Kink
