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The 9th Conference on Free Boundary Problems was held in Trento in
June 5-8, 2002. This meeting gathered 159 participants from 22
different countries including Argentina, Cuba, China, Japan, Saudi
Arabia, Taiwan. The conference registered 20 plenary lectures given by
leading scientist in the fields of modelling, analysis and numerical
treatment of PDE's, along with 7 focus sessions with three or four
speakers each and a poster session with 64 contributions. In the
opinion of most of attending people, the conference was a major event
with a large success.
Free boundary problems arise naturally in differential equations
which are defined in a domain whose boundary is a priori unknown, and
is accordingly named a "free boundary"; a further quantitative
condition must be then provided to exclude undeterminacy.
Problems of this sort arise in a large number of phenomena of
applicative interest. Examples include the classic Stefan problem, and
more general models of phase transitions: here the free boundary is
represented by the moving interface between phases. Other important
examples occur in filtration through porous media; here free boundaries
occur as fronts between saturated and unsaturated regions. Relevant
examples come from reaction-diffusion, fluid dynamics, and so on.
Free boundaries are often related to discontinuities in constitutive
relations; this raises a number of interesting analytic and numerical
questions. Existence of the solution in function spaces, uniqueness,
regularity properties, numerical approximation procedures, and other
questions have been extensively investigated. The interested reader is
referred to the proceedings of the previous editions of the series of
FBP conferences. Several of these problems are of industrial interest,
and offer opportunities of collaboration among mathematicians,
physicists, engineers, material scientists, and other applicative
scientists.
A large community of mathematicians, engineers and applicative
scientists spread over the world has been formulating and studying free
boundary problems for many years, and has been meeting regularly in a
major conference any third year or so. Actually, a list of previous
editions of this series of meetings is
* 1981 Montecatini (Italy)
* 1984 Maubuissons (France)
* 1987 Irsee (Germany)
* 1990 Montreal (Canada)
* 1993 Toledo (Spain)
* 1995 Zakopane (Poland)
* 1997 Crete (Greece)
* 1999 Chiba (Japan)
Following the tradition of the series, the 2002 conference on Free
Boundary Problems was organized in Trento in the period June 5-8, 2002,
by collecting the joint efforts of an italian-german partnership which
involved Pierluigi Colli, Gerhard Dziuk, Antonio Fasano, Karl-Heinz
Hoffmann, Jürgen Sprekels, Claudio Verdi, Augusto Visintin as direct
and contributing organizers.
The scientific committee included Michel Frémond (Paris), Avner
Friedman (Columbus, Ohio), Stephan Luckhaus (Leipzig), Marek Niezgodka
(Warsaw), John R. Ockendon (Oxford), Mario Primicerio (Firenze) and
José Francisco Rodrigues (Lisboa).
Topics covered at the Trento conference concerned problems which are
more or less directly related to free boundaries, or might be so in
perspective. Special emphasis has been put on questions of applicative
relevance: in particular, there has been a special focus on modelling,
new phenomenology, analysis of related mathematical problems,
qualitative properties of solutions, numerical issues. The list of
participants was made up of not only mathematicians but engineers,
physicists, and other applicative scientists.
To give a precise report on the topics issued and discussed during the
conference, let us detail the titles of the 20 plenary lectures, in
alphabetic order of speakers,
1. Gregoire Allaire: Structural optimization by the level set
method.
2. Luigi Ambrosio: Non linear function spaces associated to singular
perturbations.
3. Giorgio Bertotti: Magnetization modes and spin-wave instabilities in
nonlinear magnetization dynamics.
4. Zhiming Chen: Upscaling of well singularities of flow transport
through heterogeneous porous media.
5. Pierre Degond: A model for the plasma-vacuum interface.
6. Emmanuele DiBenedetto: On the selection problem for the Hele-Show
flow.
7. Wolfgang Dreyer: On nucleation and growth of liquid droplets in
single crystals.
8. Martin E. Glicksman: Dendritic growth & melting in pure
systems.
9. Nobuyuki Kenmochi: Transmission-Stefan problems arising in
Czochralski process of crystal growth.
10. Robert Kohn: Upper bounds on coarsening rates.
11. Stefan Müller: Multiscale folding patterns and energy scaling in
compressed thin films.
12. Ricardo H. Nochetto: A posteriori error control of FBPs.
13. Felix Otto: Scaling laws for the cross--tie wall.
14. Oliver Penrose: Diffusion-induced grain boundary motion : a system
with three free boundaries.
15. Errico Presutti: Phase coexistence and interfaces in statistical
mechanics.
16. Alfio Quarteroni: Fluid dynamics in blood circulation.
17. Fernando Reitich: Shape deformations and analytic continuation in
free boundary problems.
18. Alfred Schmidt: Adaptive finite element methods for phase
transition computations.
19. Victor N. Zur Starovoitov: Penalty method and problems of liquid -
solid interaction.
20. Juan José López Velazquez: Some mathematical questions on fracture
dynamics.
and the 7 focus sessions with their organizers
1. Vincenzo Capasso: Free boundary problems in polymer science,
including Martin Burger, Alessandra Micheletti and Riccardo Ricci as
speakers.
2. Vicent Caselles: Image processing, including Simon Masnou, Matteo
Novaga and Andrés F. Solé Martínez as speakers.
3. Charles M. Elliott: Grain boundary motion, including Kazuo Ito,
Barbara Niethammer and Vanessa Styles as speakers.
4. Ralph Kornhuber: Numerical aspects of free boundary problems,
including Eberhard Baensch, Folkmar A. Bornemann and Giuseppe Savarè as
speakers.
5. Masayasu Mimura: Free boundary problems in biomathematics,
including Elaine Crooks, Danielle Hilhorst and Boris Zaltzman as
speakers.
6. Georg Müller: Modelling in crystal growth, including Jeffrey J.
Derby, Michael Metzger, H.S. Udaykumar, and Georg Mueller as
speakers.
7. Peter Bates: Transitions in anisotropic materials, including
Stephen Watson, Giorgio Fusco and Adam Wheeler as speakers.
The 159 participants came from 22 different countries, with a rather
consistent participation of people from Italy, Germany, Japan, USA,
France, Britain, in particular.
The organization and success of such a big conference has been made
possible thanks to a number of supporting institutions which are
mentioned here:
Universities of Trento, Milan, Florence, Freiburg i. Br., Pavia
C.A.E.S.A.R. Institut of Bonn, W.I.A.S. Institut of Berlin Projects
"Free Boundary Problems", "Scientific Computing: ...", "Symmetries,
Geometric Structures, ..." of M.I.U.R. G.N.A.M.P.A., G.N.C.S., G.N.F.M.
of I.N.dA.M.
Proceedings of the conference will appear in the series Internat. Ser.
Numer. Math. by Birkhäuser.
Further information on the conference, including program, list of
posters, participants and all abstracts can be found on the web
page
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