Material Instabilities in Continuum Mechanics and Related Mathematical Problems
Published on 1. February 1988
Book
Hardback
544 pages
978-0-19-853273-6 (ISBN)
Description
This volume contains the proceedings of a Symposium Year on Material Instabilities in Continuum Mechanics which was organized by the Department of Mathematics, Heriot-Watt University, Edinburgh. The majority of articles in this volume concern themselves with various aspects of the mathematical theory of phase transitions in solids and fluids, and reflect the revitalization of this area of study by recent advances in the theory of systems of nonlinear partial differential equations and in the calculus of variations. These advances have led to new insights into the morphology of phase transitions (e.g. the arrangement of twins, dendrite formation) and their dynamic behaviour. The remaining articles concern related problems in solid and fluid mechanics, mathematical physics, and optimization. The volume should be of value to research workers both as a summary of the state of the art and as a source of new problems, as well as to applied mathematicians, physicists, material scientists.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Illustrations
12 figures, bibliography
ISBN-13
978-0-19-853273-6 (9780198532736)
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Schweitzer Classification
Content
Contributors; Preface; E. Acerbi and N. Fusco: An approximation lemma for W 1,p functions; E. Acerbi: Homogenization and periodic structures with holes; G. Buttazzo: Thin insulating layers: the optimization point of view; E. Cabib: Lower semicontinuity and relaxation for some problems in optimal design; G. Caginalp: Mathematical models of phase boundaries; G. Capriz: Continua with constrained or latent microstructure; D. Cioranescu and J. Saint Jean Paulin: Elastic behaviour of very thin cellular structures; B. Dacorogna and P. Marcellini: A counterexample in the vectorial calculus of variations; C. Davini: Elastic invariants in crystal theory; R.J. DiPerna: Concentrations in solutions to conservative systems; J.L. Ericksen: Some constrained elastic crystals; L.E. Fraenkel: Some results for a linear, partly hyperbolic model of viscoelastic flow past a plate; R. Illner: Derivation and validity of the Boltzmann equations: some remarks on reversibility concepts, the H-functional and coarse-graining; R.D. James: Microstructure and weak convergence; C.K.R.T. Jones: Standing waves of nonlinear Schr dinger equations: existence and stability; D. Kinderlehrer: Remarks about equilibrium configurations of crystals; J.L. Lions: Some remarks on uniqueness properties; K.A. Lurie and A.V. Cherkaev: On a certain variational problem of phase equilibrium; E. Mascolo: Some remarks on non-convex problems; D.G. McCartney and J.D. Hunt: Experimental and theoretical aspects of cellular and dendritic solidification; A. Novick-Cohen: On the viscous Cahn-Hilliard equation; O.A. Oleinik: Some asymptotic problems of linear elasticity; R.L. Pego: Phase mixtures in nonlinear viscoelasticity in one dimension; O. Penrose: Statistical mechanics and the kinetics of phase separation; M. Pitteri: On 1- and 3-dimensional models in "non-convex" elasticity; V. Roytburd and M. Slemrod: An application of the method of compensated compactness to a problem in phase transitions; R. Schianchi: A review of some non-convex problems; M.E. Schonbek: Nonlinear geometric optics and conservation laws; M. Silhav 'y: On the admissibility of shocks and propagating phase boundaries in a van der Waals fluid; F. Tomarelli: Unilateral problems in continuum mechanics; A. Visintin: Surface tension effects in phase transitions; Index.