Mathematical studies for nonlocal effect on emergence of localized patterns in dissipative systems and applications

点击翻译按钮获取中文摘要

There are various dissipative systems which are proposed as mathematical models describing pattern formations. In particular, corresponding solutions to pattern formations of reaction-diffusion systems have been much studied. In this research we have shown a new mathematical mechanism for nonlocal effects working in emergence of localized patterns. More specifically, we have studied 2-component reaction-diffusion systems with conservation of mass and proved that the nonlocal effect coming from the mass conservation is connected to the stability of the localized pattern. We also have developed the mathematical method and applied it to other model equations.