In the presence of magnetic induction and electrical fields several types of discontinuities may exist in an electrically conducting fluid. These phenomena can be described by the laws of conservation of mass, momentum, and energy; Maxwell's electromagnetic equations, and Ohm's law. Those discontinuities, which can be characterized by the conditions that both the temperature and density change across them are different from zero, are called magneto-hydrodynamic shock waves. This monograph is concerned with the study of these types of discontinuities.

The multi-component continuous approach for the investigation of the gasdynamics of a plasma is presented. More information about the flow properties of a plasma can be obtained than from the classical magnetohydrodynamic approach. Also, the resulting equations appear to be more easily solved than the Blotzmann equation of classical kinetic theory. The basic macroscopic conservation equations for a non-reacting multi-component plasma are presented. The fluid properties of each component are referred to the mean velocity of that component. Therefore, no limitations are placed on the magnitude of the diffusion velocities. The effects of electric and magnetic fields are included. The equations for a two-component mixture are used to study the structure of a shock wave in a fully-ionized hydrogen gas. It is assumed that the momentum exchange and energy exchange between the ions and electrons are important because of the strong Coulomb forces present. (Author).

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.

Fast and slow magnetohydrodynamic shock waves of arbitrary strength, for general equations of state and for arbitrary non-zero viscosity matrix, are shown to possess structure. (Author).

In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.

This book deals primarily with the basic concepts used in shock wave physics for measuring the equation of state of materials for high pressures. It provides considerably more detail in the development of the material than any competing book. The material on EOS modeling describes the basic physics models used and the form they take in hydrocodes. The models chosen are selected to show the wide variety of treatments. Written for teaching seminars, the book should benefit graduate students and interested physicists and engineers engaged in impact physics.