EI Shin-Ichiro Specially Appointed Professor

Applied Mathematics

Department of Mathematics
Research Interest
nonlinear Analysis
Asymptotic analysis, nonlinear PDE, Reaction-diffusion system

Research Activities

1The understanding of various patterns such as snow crystal, combustion, spot patterns of groups of plankton, and other kinds of chemical patterns appearing in nature are one of the most attractive objects of
study in natural science. My interest is to theoretically study the structure and mechnism of such phenomena. To do it, I use description through model equations, which is one of the most theoretical methods, well known since Newton.

The model equations which I have studied so far lie in the framework of partial differential equations which describe evolutional processes of certain materials with two mechanisms: (1) the diffusion process in space, and (2) the production and/or extinction of materials. Such model equations are generally called “reaction-diffusion systems” and their use has been well recognized in physics, chemistry, biology and other fields from a mathematical modelling point of view.

It is important to have interests in patterns appearing in nature, which give a strong motivation and conatus for learning in our laboratory. I welcome such students.


  • S.-I. Ei and E. Yanagida, Slow dynamics of interfaces in the Allen-Cahn equation on a strip-like domain, SIAM J. Math. Anal. vol. 29(1998), 555-595.
  • S.-I. Ei, The motion of weakly interacting pulses in reaction-diffusion systems, J.D.D.E. 14(1) (2002), 85-137.
  • S.-I. Ei, M. Mimura and M. Nagayama, Interacting Spots in reaction diffusion systems, DCDS 14 (2006), 31-62.