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Greeting as a Guest of Honor

Greeting as a Guest of Honor. Hiroshi Fujita. University of Tokyo (Prof. Emeritus). The Fourth Euro-Japanese Workshop on Blow-up September 6-10, 2010: Lorentz Center, Leiden, the Netherlands. Gratitude:. 1) to WS organizers, Professors M. Fila, J. Hulshof ,

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Greeting as a Guest of Honor

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  1. Greeting as a Guest of Honor Hiroshi Fujita University of Tokyo (Prof. Emeritus) The Fourth Euro-Japanese Workshop on Blow-up September 6-10, 2010: Lorentz Center, Leiden, the Netherlands

  2. Gratitude: 1) to WS organizers, Professors M. Fila, J. Hulshof , J.L. Vazquez and E. Yanagida 2) to WS coordinator, Ms. Pauline Vincenten

  3. My Particular Excitement: Participating in this WS here, I am particularly excited, (1) To witness extensive current progresses in the Blow-up Study for which I made an initial work in 1966, 44 years ago. (2) To reflect on the strong link between Holland and Japan since 17th century.

  4. Old link between the Netherlands and Japan In 17th century, Tokugawa shogunate closed the country's door to all Westerners except for Dutch persons until the middle of 19th century. During Edo period, Western civilization and culture was conveyed to Japan only by Dutch officers working at Holland Trading House in Dejima, Nagasaki. As a typical example of those Dutch intellectuals, Philipp Franz von Siebold（1796-1866）is well-known in Japan and, probably, in Leiden, too. This contribution by Dutch experts during Edo period paved a way for a rush and successful import of Western knowledge to Japan and contributed much to modernization of Japanese system after Meiji Restoration (1868),

  5. Role of Blow-up Study in 21st Century Mathematics in the 21st century is expected to challenge deep, complicated, over-arching problems arising from science, technology and society. It must be developed in the spirit of mathematical sciences but I believethat nonlinear analysis to pursue global behaviors and drastic changes of the solution will play a core role in mathematical activities, the blow-up study being its leading part. Obviously, mathematics is an indispensable basis of new sciences, e.g. global ecology. Nonlinear analysis is expected to offer mathematical methodology for arising fields such as bio-medical sciences and bio-informatics.

  6. Charms of Blow-up Study (and of Nonlinear Analysis in general). Charm 1.Realistic motivations can lead to charming and challenging problems and theorems. Fifty years ago, I struggled for the Navier-Stokes equation, particularly，for the still formidable question of the global existence of 3D solutions, while the 2D problems are OK. Then in order to think over joint influence of the degree of nonlinearity and the space dimension for parabolic equations, I tried to consider simplified but typicalexamples and reached the following initial value problem.

  7. Comment on the naming of the equation: Here,I wish to express my thanks to those who call the equation above, Fujita's equation. Namely, thanks for their friendly consideration of the historical course of the matter. I should feel hesitation in calling it so by myself, due to some sense of Oriental modesty. The equation is, however, too specific to be called a semi-linear parabolic equation.

  8. Charm 2.In nonlinear analysis, mathematicians can experience joy of discovery of un-expected result as well as joy of creation of new methods of proof. In fact, when I started my study of Fujita equation, there was no conjecture or numerical experiments which suggest the existence of a single exponent which controls the blowing-up situation as follows.

  9. Charm 3. It is a good stage where challenging collaboration with numerical experiments. For nonlinear analysis like blow-up study, significant numerical analysis is difficult to carry out. Often, it requires developments of numerical methods. The situation is similar to the relationship between theory and experiment in physics. Theoretical analysis and numerical experiments can jointly stimulate mathematicians' imagination and deepen their insight to to solve the problem. This would be characteristic to promising fields of mathematical sciences in 21st century.

  10. This is what I want to say.Thank you.

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