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This volume introduces a systematic approach to the solution of
some mathematical problems that arise in the study of the
hyperbolic-parabolic systems of equations that govern the motions
of thermodynamic fluids. It is intended for a wide audience of
theoretical and applied mathematicians with an interest in
compressible flow, capillarity theory, and control theory. The
focus is particularly on recent results concerning nonlinear
asymptotic stability, which are independent of assumptions about
the smallness of the initial data. Of particular interest is the
loss of control that sometimes results when steady flows of
compressible fluids are upset by large disturbances. The main ideas
are illustrated in the context of three different physical
problems: (i) A barotropic viscous gas in a fixed domain with
compact boundary. The domain may be either an exterior domain or a
bounded domain, and the boundary may be either impermeable or
porous. (ii) An isothermal viscous gas in a domain with free
boundaries. (iii) A heat-conducting, viscous polytropic gas.
The International Society for the Interaction of Mechanics and
Mathematics has a long-standing and respected tradition of hosting
symposia that provide a forum for disseminating new developments
and methods. Trends in Applications of Mathematics to Mechanics
represents the proceedings of the eleventh such symposium, held at
the University of Nice in May 1998.
Comprising invited lectures and refereed papers, this volume
includes recent results that open perspectives on fields in
mechanics and their methodological counterparts in mathematics. It
also surveys important advances in the areas where mathematics and
mechanics interact. The applications addressed include:
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