J.L. Ericksen – författare

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.

The Institute for Mathematics and Its Applications was established by a grant from the National Science Foundation to the University of Minnesota in 1982. The IMA seeks to encourage the development and study of fresh mathematical concepts and questions of concern to the other sciences by bringing together mathematicians and scientists from diverse fields in an atmosphere that will stimulate discussion and collaboration. The IMA Volumes are intended to involve the broader scientific community in this process.

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 AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part 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: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe­ cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

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.