- Volume
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: us ISBN 9780387941110
Description
This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un- known domain, an additional condition must be prescribed on the free boundary.
A classical example is the Stefan problem of melting of ice; here the temperature sat- isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera- ture within the water. Some free boundary problems lend themselves to variational formulation.
Table of Contents
Free boundary problems arising in industry.- Convex free boundaries and the operator method.- The space SBV(?) and free discontinuity problems.- Wiener criterion for the obstacle problem relative to square Hormander's operators.- Asymptotic behavior of solidification solutions of Stefan problems.- Blow-up and regularization for the Hele-Shaw problem.- A multidomain decomposition for the transport equation.- Axisymmetric MHD equilibria from Kruskal-Kulsrud to Grad.- A two-sided game for non local competitive systems with control on source terms.- The Stefan problem with surface tension.- The Rayleigh instability for a cylindrical crystal-melt interface.- Towards a unified approach for the adaptive solution of evolution phase changes.- Blowup and global existence for a non-equilibrium phase change process.
- Volume
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: gw ISBN 9783540941118
Description
This volume contains articles based on recent research in variational and free boundary problems, as collected by the Institute for Mathematics and its Applications. The collection as a whole concentrates on novel applications of variational methods to applied problems. The articles are based on models which arise in phase transitions, elastic/plastic contact problems, Hele-Shaw cells, crystal growth, variational formulation of computer vision models, magneto-hydrodynamics, bubble growth, hydrodynamics (jets and cavities), and stochastic control and economics. They represent mathematical methods which can be further extended and developed for other models.
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