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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis The Shock Development Problem
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The Shock Development Problem
Demetrios Christodoulou (Gebundene Ausgabe, Englisch)
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Beschreibung
This monograph addresses the problem of the development of shocks in the context of the Eulerian equations of the mechanics of compressible fluids. The mathematical problem is that of an initial-boundary value problem for a nonlinear hyperbolic system of partial differential equations with a free boundary and singular initial conditions.
The free boundary is the shock hypersurface and the boundary… conditions are jump conditions relative to a prior solution, conditions following from the integral form of the mass, momentum and energy conservation laws. The prior solution is provided by the author‘s previous work which studies the maximal classical development of smooth initial data. New geometric and analytic methods are introduced to solve the problem. Geometry enters as the acoustical structure, a Lorentzian metric structure defined on the spacetime manifold by the fluid. This acoustical structure interacts with the background spacetime structure. Reformulating the equations as two coupled first order systems, the characteristic system, which is fully nonlinear, and the wave system, which is quasilinear, a complete regularization of the problem is achieved.
Geometric methods also arise from the need to treat the free boundary. These methods involve the concepts of bi-variational stress and of variation fields. The main new analytic method arises from the need to handle the singular integrals appearing in the energy identities. Shocks being an ubiquitous phenomenon, occuring also in magnetohydrodynamics, nonlinear elasticity, and the electrodynamics of noninear media, the methods developed in this monograph are likely to be found relevant in these fields as well. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.01.2019
Sprache
Englisch
EAN
9783037191927
Herausgeber
EMS Press
Serien- oder Bandtitel
EMS Monographs in Mathematics
Sonderedition
Nein
Autor
Demetrios Christodoulou
Seitenanzahl
932
Auflage
1
Einbandart
Gebundene Ausgabe
Schlagwörter
development of shocks, free boundary problems, nonlinear hyperbolic partial differential equations, mechanics of compressible fluids
Thema-Inhalt
PBKL - Integralrechnung und -gleichungen
Höhe
235 mm
Breite
16.5 cm
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