عنوان

The shock development problem /

شابک

3037196920

شابک

9783037196922

شابک اشتباه

3037191929

شابک اشتباه

9783037191927

عنوان اصلي

The shock development problem /

نام عام مواد

[Book]

نام نخستين پديدآور

Demetrios Christodoulou.

محل نشرو پخش و غیره

Zürich, Switzerland :

نام ناشر، پخش کننده و غيره

European Mathematical Society,

تاریخ نشرو بخش و غیره

[2019]

نام خاص و کميت اثر

1 online resource (932 pages)

عنوان فروست

EMS Monographs in Mathematics

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

عنوان

Shock development problem.

شماره استاندارد بين المللي کتاب و موسيقي

9783037191927

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential equations.

موضوع مستند نشده

Fluid mechanics.

موضوع مستند نشده

Shock waves-- Mathematical models.

موضوع مستند نشده

Differential equations, Partial.

موضوع مستند نشده

Differential equations.

موضوع مستند نشده

Fluid mechanics.

موضوع مستند نشده

Fluid mechanics.

موضوع مستند نشده

MATHEMATICS-- Calculus.

موضوع مستند نشده

MATHEMATICS-- Mathematical Analysis.

موضوع مستند نشده

Partial differential equations.

موضوع مستند نشده

Shock waves-- Mathematical models.

موضوع مستند نشده

MAT-- 005000

موضوع مستند نشده

MAT-- 034000

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Christodoulou, Demetrios

تاريخ عمليات

20200823094818.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y