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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time (Paperback, Softcover reprint of hardcover 1st ed. 1994)
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Discovery Miles 44 850
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Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Series: Mathematical Physics Studies, 14
Expected to ship within 10 - 15 working days
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Total price: R4,505
Discovery Miles: 45 050
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For seventy years, we have known that Einstein's theory is
essentially a theory of propagation of waves for the gravitational
field. Confusion enters, however, through the fact that the word
wave, in physics, implies sometimes repetition and sometimes not.
This confusion is often increased by he use of Fourier transforms,
by which a disturbanse which appears to be without repetition is
resolved into periodic wave-trains with all frequencies. But, in a
general curved space-time, we have nothing corresponding to Fourier
transforms. Here, we consider systematically waves corresponding to
the propagation of discontinuities of physical quantities
describing either fields (essentially electromagnetic fields and
gravitational field), or the motion of a fluid, or together, in
magnetohydrodynamics, the changes in time of a field and of a
fluid. The main equations, for the different studied phenomena,
constitute a hyperbolic system and the study of a formal Cauchy
problem is possible. We call ordinary waves the case in which the
derivative of superior order appearing in the system are
discontinuous at the traverse of a hypersurface, the wave front ;
we call shock waves the case where the derivatives of an order
inferior by one are discontinuous at the traverse of a wave front.
XI xii PREFACE From 1950, many well-known scientits (Taub, Synge,
Choquet-B ruhat, etc.) have studied the corresponding equations for
different physical phenomena : systems associated to the
electromagnetic and gravitational fields, to hydrodynamics and to
magnetohydrodynamics.
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