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The heh~vior of matter anrl waves in a rlynamical setting nffer~
many challenging prohlems to the mathematician anrl the m~terials
scientist alike. Unrler review in this volume are a variety of
nonlioear phenomena whose con- sirleration entails new
perspectives, oot commooly fouorl in the literatllre. Of particular
note is the experimental aspect of many of the papers. In
arlrlition, attention has been given ta the interaction of
electromagnetic anrl mechanical pro- perties of materials.
Ouestions arise which cannat naw he answererl. Attempts are marle
to rlescrihe anrl to unrlerstand phenomena which are far from
equilihrium ar which suffer ahrupt changes in behavior. Some of
this requires tentative physical or aoalytical assumptions. The
hases for these hypotheses lie in the quest for a rational theory
which agrees with experiment. This Volume anr! Volume 2, ~scUJation
theory, compution, an'!. methorls ~ com- pensated ~~mpact~ess,
offer oi fferent vi ewpoi nts of some of the rlynami cal stllrli es
considereo during the 19f14-19R5 IMA program, Continullm Physics
and Partial Differenti al Equati ons. Contents of the other
volumes, fOllnrl at the enrl of the hook, contain other relevant
titles.
This IMA Volume in Mathematics and its Applications Oscillation
Theory, Computation, and Methods of Compensated Compactness
represents the proceedings of a workshop which was an integral part
of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL
DIFFERENTIAL EQUATIONS. We are grateful to the Scientific
Committee: J. L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for
their dedication and hard work in developing an imaginative,
stimulating, and productive year-long program. George R. Sell Hans
Weinberger PREFACE Historically, one of the most important prohlems
in continuum mechanics has been the treatment of nonlinear
hyperbolic systems of conservation laws. Thp. importance of these
systems lies in the fact that the underlyinq equ~tions of mass,
momentum, and energy are descrihed by conservation laws. Their
nonlinearity and hyperbolicity are consequences of some cornmon
constitutive relations, for example, in an ideal gas. The I. M. A.
Workshop on "Osci 11 at i on theory. computat i on, and methods of
com- pensated compactness" brought together scientists from both
the analytical and numerical sides of conservation law research.
The goal was to examine recent trends in the investigation of
systems of conservation laws and in particular to focus on the
roles of dispersive and diffusive limits for singularily perturbed
conservation laws. Special attention was devoted to the new ideas
of compen- sated compactness and oscillation theory.
The heh~vior of matter anrl waves in a rlynamical setting nffer~
many challenging prohlems to the mathematician anrl the m~terials
scientist alike. Unrler review in this volume are a variety of
nonlioear phenomena whose con- sirleration entails new
perspectives, oot commooly fouorl in the literatllre. Of particular
note is the experimental aspect of many of the papers. In
arlrlition, attention has been given ta the interaction of
electromagnetic anrl mechanical pro- perties of materials.
Ouestions arise which cannat naw he answererl. Attempts are marle
to rlescrihe anrl to unrlerstand phenomena which are far from
equilihrium ar which suffer ahrupt changes in behavior. Some of
this requires tentative physical or aoalytical assumptions. The
hases for these hypotheses lie in the quest for a rational theory
which agrees with experiment. This Volume anr! Volume 2, ~scUJation
theory, compution, an'!. methorls ~ com- pensated ~~mpact~ess,
offer oi fferent vi ewpoi nts of some of the rlynami cal stllrli es
considereo during the 19f14-19R5 IMA program, Continullm Physics
and Partial Differenti al Equati ons. Contents of the other
volumes, fOllnrl at the enrl of the hook, contain other relevant
titles.
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