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Free Boundary Problems in Industry

17th July 2000 to 4th August 2000

Organisers: N Barton (Sydney), EJ Hinch (Cambridge), JR Ockendon (Oxford)

Programme Theme

Free Boundary Problems (FBPs) are, as the name suggests, problems that need to be solved in regions whose boundaries are unknown a priori and have to be determined as part of the solution. They thus involve the modelling and analysis of both bulk and surface phenomena, where the "surface" may range from that of a block of melting ice to an optimal stopping time. The topic "Free Boundary Problems" would not exist as a distinct mathematical entity without the stimulus it received from industrial research in the 1970's. The industrial demand for better understanding of free boundary problems, especially diffusional ones like Stefan problems, has brought about a startling unification in the mathematical and numerical analysis of models for phenomena such as shock waves, water waves, flame propagation, phase transformations and elastic contact phenomena. In particular it stimulated the search for weak and variational methods with which to prove well-posedness and to suggest robust and efficient algorithms that can be adapted to suit industrial needs.

It is very satisfying that recent developments in the mathematical theory of FBPs have given completely new insights into both regularity theories for partial differential equations and into the mathematical modelling of basic phenomena such as phase transitions and pattern formation, as well as equipping the community with off-the-shelf algorithms that answer many of the problems that spawned the subject 30 years ago

This programme will pivot around workshop-style sessions in which industrial and academic researchers will meet informally to discuss the latest generation of free boundary problems that need to be confronted theoretically. Coherence will be provided by considering problems from the food industry in one week, the glass industry in a second week and the metal industry in a third week. There will also be a small number of expository lectures on the relevant problems and methodologies.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons