Variational and Free Boundary Problems

✍ Scribed by Avner Friedman (auth.), Avner Friedman, Joel Spruck (eds.)

• Publisher: Springer-Verlag New York
• Year: 1993
• Tongue: English
• Leaves: 209
• Series: The IMA Volumes in Mathematics and its Applications 53
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xv
Free Boundary Problems Arising in Industry....Pages 1-10
Convex Free Boundaries and the Operator Method....Pages 11-27
The Space SBV(Ω) and Free Discontinuity Problems....Pages 29-45
Wiener Criterion for the Obstacle Problem Relative to Square Hörmander’s Operators....Pages 47-62
Asymptotic Behavior of Solidification Solutions of Stefan Problems....Pages 63-72
Blow-Up and Regularization for the Hele-Shaw Problem....Pages 73-85
A Multidomain Decomposition for the Transport Equation....Pages 87-109
Axisymmetric MHD Equilibria from Kruskal-Kulsrud to Grad....Pages 111-134
A Two-Sided Game for Non Local Competitive Systems with Control on Source Terms....Pages 135-152
The Stefan Problem with Surface Tension....Pages 153-157
The Rayleigh Instability for a Cylindrical Crystal-Melt Interface....Pages 159-169
Towards a Unified Approach for the Adaptive Solution of Evolution Phase Changes....Pages 171-193
Blowup and Global Existence for a Non-Equilibrium Phase Change Process....Pages 195-204

✦ Subjects

Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization