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Metastability and Incompletely Posed Problems 1987 ed. [Kõva köide]

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This IMA Volume in Mathematics and its Applications Metastability and Incompletely Posed Problems represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EOIIATIONS. We are grateful to the Scientific Committee: ,I.L. Eri cksen D. Kinderlehrer H. Rrezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger Preface Most equilibrium events in nature do not realize configurations of minimum energy. They are only metastable. Available knowledge of constitutive relations and environmental interactions may be limiterl. As a result, many configurations may he compatible with the rlata. Such questions are incompletely poserl. The papers in this volume address a wide variety of these issues as they are perceived by the material scientist and the mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computation.
Dissipative Mechanisms.- Does Rank-One Convexity Imply Quasiconvexity?.-
Metastable Harmonic Maps.- Bifurcation of Constrained Problems in
Thermoelasticity.- The Compressible Reynolds Lubrication Equation.- Twinning
of Crystals I.- Quasiconvexity and Partial Regularity in the Calculus of
Variations.- to Pattern Selection in Dendritic Solidification.- Some Results
and Conjectures in the Gradient Theory of Phase Transitions.- The Stability
and Metastability of Quartz.- Continuation Theorems for Schrodinger
Operators.- Twinning of Crystals II.- Simulation of Pseudo-Elastic Behaviour
in a System of Rubber Ballons.- Asymptotic Problems in Distributed Systems.-
Stability of Nonlinear Waves.- The Nash-Moser Technique for an Inverse
Problem in Potential Theory Related to Geodesy.- Variational Stability and
Relaxed Dirichlet Problems.- A Contribution to the Description of Natural
States for Elastic Crystalline Solids.- Nonlocal Problems in
Electromagnetism.- Hyperbolic Aspects in the Theory of the Porous Medium
Equation.- Greens Formulas for Linearized Problems with Live Loads.- Some
Aspects of Adiabatic Shear Bands.- Information about other Volumes in this
Program.