This was the 4th edition of a series of Euro-Japanese workshops on blow-up
phenomena. Initiated by a collaboration between European and Japanese
scientists working in the field of semilinear parabolic equations, an area
motivated in part by the early attempts to understand singularity formation in
the solutions of the Navier- Stokes equations and the
onset of turbulence in fluid flows, these workshops reach out to application
areas in which the occurrence or non-occurence of
blow-up is a fundamental issue. Once blow-up is established, the main questions
are when, where and how does it occur, as well as what happens after blow-up.
More precisely, in order to understand the singularity formation, it is natural
to investigate the blow-up time, blow-up set, blow-up profile in time and space
and whether or not the solution can be continued beyond the blow-up time.
The aim of this workshop was to bring together leading researchers in the field
of semilinear parabolic equations, and various other
fields related to blow-up (such as fluid mechanics, mathematical biology,
geometric flows), as well as junior scientists. There were a total of 41
registered participants from 8 European countries and Japan, 14 of them are
PhD-students or post-docs. During the workshop, 19 invited speakers gave longer
talks (45 min.) and 9 young researchers presented short talks (15 min.). The
talks fuelled vivid discussions during and after the presentations and also in
smaller circles during the breaks and during the time reserved for discussions.
Several papers were initiated or worked on.
The workshop in Leiden will be followed by a new one in France in two years
We acknowledge the excellent working environment and organizational support of
the Lorentz Center staff, in particular Pauline Vincenten. We are grateful for
the financial support provided by the Lorentz Center, KNAW, Stieltjes
Institute and NDNS+.
M. Fila (Bratislava, Slovakia)
J. Hulshof (Amsterdam, The Netherlands)
J.L. Vazquez (Madrid, Spain)
E. Yanagida (Tokyo, Japan)