Details

Autor(en) / Beteiligte

• Spruck, Joel,
• Friedman, Avner,

Titel

Variational and free boundary problems

Auflage

1st ed. 1993

Ort / Verlag

New York, New York : Springer,

Erscheinungsjahr

[1993]

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• Includes bibliographical references.
• 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 Hörmander’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.
• 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 unknown 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 satisfies 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 temperature within the water. Some free boundary problems lend themselves to variational formulation.
• English
• Description based on print version record.