Fokker-Planck equations that describe the evolution of phase distributions in coupled oscillators were treated under an asymmetric natural frequency distribution. We found that the destabilization of the trivial distribution is of Hopf bifurcation...

In this research project, systems of reaction-diffusion (convection) equations are investigated from a viewpoint of singular limit analysis. The results obtained are summarized as follows.
1. In spherically symmetric multidimensional domains, reac...

Our results may be summarized as follows
1.First, we studied from the viewpoint of functional analysis the problem of construction of Markov processes with boundary conditions in probability theory. Our approach is distinguished by the extensive u...

We have carried out theoretical analysis and development of numerical method for studying various macroscopic and microscopic pattern formation in material sciences. In particular, we have investigated both numerically and analytically
(1) structu...