Montecatini Terme, 10-12 giugno 2004

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where you can register and apply for a short talk. No registration fee is required.

INVITED SPEAKERS Gregoire Allaire, Peter Bates, Juan Casado-Diaz, Alain Damlamian, Emmanuele DiBenedetto, Eduard Feireisl, Miguel Angel Herrero, Nobuyuki Kenmochi, Stephan Luckhaus, Masayasu Mimura, Francois Murat, Gabriel Nguetseng, Adelia Sequeira, Songmu Zheng FREE BOUNDARY PROBLEMS These are boundary-value problems for differential equations, which are set in a domain whose boundary is a priori unknown, and is accordingly named a free boundary . Problems of this sort arise in a large number of phenomena of applicative interest, and have been the object of intense research in the last forty years. This conference is devoted to three topics that are certainly prominent for applications of free boundary problems. BIOMATHEMATICS Biology and medicine are becoming more and more important sources of interesting and stimulating mathematical problems. Cell populations, cancer growth and therapies, hemodynamics and other branches of physiology and biology are remarkable fields of application of P.D.E.'s with frequent inclusion of free boundaries. MULTISCALING The use of two or more length-scales occurs in a natural way in the construction of mathematical models for various phenomena. Composite materials are a typical example, since their state depends on both macroscopic and microscopic variables. In the last years the analysis of multi-scale models has seen a rapid growth. The by-now classic theory of homogenization yields effective macroscopic descriptions of these phenomena. The recently developed technique of two-scale convergence provides a rigorous foundation for the engineering method of asymptotic expansions. INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS Dynamical systems have been attracting the attention of scientists for more than a century. For a long time studies have been mainly directed towards finite-dimensional systems, which are typically represented by O.D.E.s. In recent years attention to infinite-dimensional aspects has been growing, and remarkable progresses have been accomplished in the analysis of the long-time behavior of solutions of P.D.E.s.