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Host: LOrentz Center
Homepage: http://www.lc.leidenuniv.nl/lorentz_center/2001/20010312/info.php3?wsid=6, http://www.math.u-psud.fr/~gtanl/Leiden/
Organizers: D. Hilhorst (Orsay, France), H. Matano (Tokyo, Japan)
Description:
The meeting will deal with a variety of reaction-diffusion systems of second or fourth order, possibly involving nonlocal
terms. Those systems appear as reliable mathematical models for various key phenomena in science and engineering,
such as segregation or aggregation of biological populations, spatio-temporal patterns in chemical reactions, phase
transitions in alloys and microphase separation of diblock copolymers.
Many of those systems of equations involve small parameters either in the diffusion terms or in the reactions terms. Of special interest is the singular limits of those systems that appear as the parameters tend to zero. The limit problems typically involve free boundaries separating the spatial region into domains of different solution phases; the free boundaries can therefore be regarded as 'interfaces' between different phases. In other typical situations, solutions of the systems develop spike-shaped patterns that converge to Dirac-measure-like singularities as the parameters tend to zero.
It is important that such singular behaviors are not accidental pathological phenomena, but are the essential features of the systems that we study. Deriving the limit problems by formal and/or rigorous asymptotic analysis is often a challenging goal, but understanding the nature of the limit problems themselves is equally important. The main themes of the meeting include, among other things, the following:
deriving and/or studying the free boundary problems that appear in the singular limit; studying spike patterns, particularly the location of spikes and the interaction between them.
Date received: December 21, 2000
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