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Full Description
This monograph collects research and expository articles reflect- ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ- ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co- ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles University of Thessaloniki, the University of Florence, the University of Lisbon and the University of Oxford. This project was carried out under the title "Mathemat- ical Models of Phase Transitions and Numerical Simulation" , in the framework of twinning program for stimulation of cooperation and scientific interchange, sponsored by the European Community.
The underlying idea of the project was to create and study the mathematical models arising in applied engineering problems with free boundaries in a broad sense, namely in melting and freezing problems, diffusion-reaction processes, solid-solid phase transition, hysteresis phenomena, "mushy region" descriptions, contact prob- lems with friction andjor adhesion, elastoplastic deformations, etc. vi This large spectrum of applied problems have in common the main feature of brusque transitions of their qualitative behaviour that correspond, in general, to non-classical discontinuous monotone or non monotone strong nonlinearities in the mathematical equations.
Contents
I — Generalized Phase Changes.- Internal constraints and constitutive laws, by M. Frémond.- Liquid-vapour phase change in porous media, by P. Nicolas.- The Cahn-Hilliard model for the kinetics of phase separation, by C.Elliott.- An evolution problem related to shape memory alloys, by P. Colli.- Automatic control of one-dimensional thermomechanical phase transitions, by J. Sprekels.- Irreversible phase changes, by D. Blanchard.- Phase change without sharp interfaces, by A. Fasano and M. Primicerio.- II — Stefan Problems.- The Stefan problem revisited, by J.F. Rodrigues.- Stefan problem with surface tension, by A. Visintin.- On the singularities of one-dimensional Stefan problems with supercooling, by A. Fasano, M. Primicerio, S.D. Howison and J.R. Ockendon.- Kinetic undercooling regularization of supercooled Stefan problems, by S. Howison and Xie W..- Two-phase Stefan problems with feedback controls, by K.-H. Hoffmann and N. Kenmochi.- Local mesh refinements for two-phase Stefan problems in two space variables, by R.H. Nochetto, M. Paolini and C. Verdi.- Linearization of parabolic free boundary problems, by R.H. Nochetto.- III - Miscellaneous Problems.- Externally induced dissipative collision, by M.M Marques.- Optimal control of systems governed by hemivariational inequalities, by P.D. Panagiotopoulos and J. Haslinger.- A mathematical formulation for a generalized Hertz impact problem, by J.A.C Martins and L. Trabucho.- Free boundary value problems arising in composite masonry structures, by C.C. Baniotopoulos.- On uniqueness for evolution problems with hysteresis, by M. Hilpert.- A diffusion problem with gradient constaint, by L. Santos.- AUTHOR INDEX.
