Dynamical Problems in Continuum Physics

ISBN-13: 9781461269991 / Angielski / Miękka / 2013 / 330 str.

J. L. Bona; C. Dafermos; J. L. Ericksen

Opis

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.

Spis treści

Solitary Water-Waves in the Presence of Surface Tension.- Presence and Absence of Weak Singularities in Nonlinear Waves.- Some Dynamical Problems in Continuum Physics.- Existence and Asymptotic Behavior for Strong Solutions of the Navier Stokes Equations in the Whole Space.- A Confluence of Experiement and Theory for Waves of Finite Strain in the Solid Continuum.- Interaction of Shallow-Water Waves and Bottom Topography.- Classical Piezoelectricity: Is the Theory Complete?.- On the Dynamics of a Collisionless Plasma.- Acoutoelasticity.- One Dimensional Finite Amplitude Pulse Propagation in Electroelastic Semiconductors.- Weak Solutions of Transonic Flow by Compensated Compactness.- Extended Thermodynamics of Ideal Gases.- Phase Transitions in One Dimensional Nonlinear Viscoelasticity: Admissibility and Stability.- Dynamic Phase Transitions and Compensated Compactness.- Recent Advances in Nonlinear Wave Equations.- Some Existence, Uniqueness, and Non-Uniqueness Results for Weakly Hyperbolic Equations in Gevrey Classes.- Information About Other Volumes in this Program.