Shock waves /

"This book presents the fundamentals of the shock wave theory. Shock waves are present in many natural situations as a consequence of nonlinear constitutive relations. Mathematical analysis of shock waves is based mostly on the conservation laws. Consider the case of gas dynamics. There is th...

Ausführliche Beschreibung

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Weitere Titel:
Introduction
Preliminaries
Scalar convex conservation laws
Burgers equation
General scalar conservation laws
System of hyperbolic conservation laws, general theory
Riemann problem
Wave interactions
Well-posedness theory
Viscosity
Relaxation
Nonlinear resonance
Multi-dimensional gas flows
Concluding remarks
1. Verfasser:
Liu, Tai-Ping
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
Providence, Rhode Island : American Mathematical Society, [2021]
Zusammenfassung:
"This book presents the fundamentals of the shock wave theory. Shock waves are present in many natural situations as a consequence of nonlinear constitutive relations. Mathematical analysis of shock waves is based mostly on the conservation laws. Consider the case of gas dynamics. There is the conservation of mass. The conservation of momentum follows from the Newtonian physics. During the nineteenth century, the conservation of energy and the second law of thermodynamics were formulated. This is the scientific background when Stokes [119] and Riemann [112] did their pioneering works on shock waves in the mid-nineteenth century. More conservation laws were subsequently formulated with the study of electro-magnetism, nonlinear elasticity, high temperature gas dynamics, and other physical phenomena. There have been important, continuing progresses on the development of shock wave theory since the time of Stokes and Riemann."--
Umfang:
1 online resource (pages cm.)
Mode of access : World Wide Web
Format Details:
Mode of access : World Wide Web
Bibliografie:
Includes bibliographical references and index.
Schriftenreihe:
Graduate Studies in Mathematics,
Sekundärform:
Publikations­art: Electronic reproduction.
Verlag: Providence, Rhode Island :: American Mathematical Society.
Publikations­datum: 2021
ISBN:
9781470466244 (online)
ISSN:
1065-7339
DOI:
10.1090/gsm/215
Zugangseinschränkungen:
Access is restricted to licensed institutions
Schlagworte:
Shock waves > Mathematical models.
Partial differential equations > Hyperbolic equations and systems > Hyperbolic conservation laws.
Partial differential equations > Hyperbolic equations and systems > Shocks and singularities for hyperbolic equations.
Partial differential equations > Hyperbolic equations and systems > First-order hyperbolic systems.
Fluid mechanics > Shock waves and blast waves in fluid mechanics > Shock waves and blast waves in fluid mechanics.
Fluid mechanics > Compressible fluids and gas dynamics, general > Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics.
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