Name : Monobe, Harunori (物部治徳)
Affiliation : Department of Mathematics, Graduate School of Science / Faculty of Science, Osaka Metropolitan University
Position : Associate Professor
E-mail : monobe[at]omu.ac.jp
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Research interests
Traveling waves for free boundary problems and interface equations
Analysis of a fully nonlinear parabolic equation related to the groove profile in crystal grain regions
Relation between mean curvature flow with driving force and reaction diffusion systems
Analysis of the spread and dynamics of populations, e.g., controlling invasive alien species
Interface equations and free boundary problems appear in various mathematical models describing natural phenomena, e.g., melting of ice, crystal growth of materials, population dynamics and so on. In general, it's hard to understand the behavior of solutions to them because the interfaces may occur topological change. In order to understand that , the analysis of special solutions to them, such as ``entire solutions'', is of importance. For instance, traveling wave solutions for interface equation and partial differential equations are well-studied and there are a lot of results. However, most of them are defined in whole spaces of 1 -D. As typical examples of traveling waves defined in 2-D, we can find ``Grim Reaper" and ``V-shaped traveling fronts" but there are also defined in whole spaces. Meanwhile, a lot of traveling waves composed of closed curves and surfaces are observed in natural phenomena, e.g., oil droplet and cell locomotion. From this reason, it is expected that what we understand the structure of such traveling waves is important.
The main theme of my research is to study the structure of traveling waves, composed of closed manifolds, to interface equations and free boundary problems. Also I am interested in the analysis of a fully nonlinear parabolic equation related to the groove profile in crystal grain regions, Stefan-like problems related to population dynamics and singular limit problems of reactions-diffusion systems.
Traveling wave composed of Jordan curve for a free boundary problem
( Japanese Version )
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