Nonequilibrium, nonlinear, ill-posedness, and hierarchy

Takashi Suzuki
  Main subjets of research
[1]Analysis and modeling of nonlinear phenomena
[2]Ill-posed Problem
[3]Vaiational Problem
[4]Mathematical Medicine

[Objective]
 Problems of basical science(physicas, chemistry, and biology) and applied science(engineering and medicine) have mathematical similarities. At our laboratory, we solve these problems by using mathematical model.
 
[Method]
 It is a starting point in mathematical model research to describe actual problems by mathematical equations. We are treating two-directional modelings, top down and bottom up modelings. In the bottom up modeling, one derives mean field equation from micro state. In the top down modeling, on the other hand, one describes equation from macroscopic principles. Many interesting phenomena are observed by simulations of the mathematical equations derived. Then, we start mathematics which dominate these phenomena. Furthermore, we open up our research area by analytical study, revealing depthful principles, such as "quantized blowup mechanism", "cyclic hierarchy", "duality between fields and particles", and so on. Our study also aims to educate undergraduate and graduate students. Training of research staff progresses studies of projects. The current projects are "Nonlinear Technical Science" based on Osaka University School of Engineering and Science and Osaka University, "National Congress of Theoretical and Applied Mechanics", "New Twistof Variational Problem", "Mathematical Medicine", "The East Asia PDE Conference " which PDE researcher at East Asia held, and so on. In this laboratory, there are some foreign students and research fellows through the CREST project "Mathematical Medicine Develops Tumor Growth Explications and Medical Technology Innovations" by JST, and "Marie Curie Action" international research student exchange program.
 
[Basic]
 I wrote books [3,4] about mathematical and numerical analyses. In the first semester, depending on students' backgrounds, we gather materials for their studies, train their foundation for analysis through standard textbooks about mathematical and numerical analyses, select their subjects of studies, and start their studies.
 
[1] Mean Field Theories and Dual Variation, Atlantis Press, Amsterdam-Paris, 2008.
[2] Free Energy and Self-Interacting Particles, Birkhauser, Boston, 2005.
[3] Applied Analysis : Mathematical Methods in Natural Science, Imperior College Press, London, 2004 .
[4] Operator Theory and Numerical Methods, North-Holland, Amsterdam, 2001.