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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."
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 volume contains the proceedings from the International
Conference on Nonlinear Evolutionary Partial Differential Equations
held in Beijing in June 1993. The topic for the conference was
selected because of its importance in the natural sciences and for
its mathematical significance. Discussion topics include
conservation laws, dispersion waves, Einstein's theory of
gravitation, reaction-diffusion equations, the Navier-Stokes
equations, and more. New results were presented and are featured in
this volume. Titles in this series are co-published with
International Press, Cambridge, MA.
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