Scientific Report

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 from now.

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)