Hiroshi Matano

Hiroshi Matano was born in Kyoto and graduated Kyoto University. His major was mathematical sciences. His first academic position was at the University of Tokyo, then he moved to Hiroshima University. After that, he spent 30 years at the University of Tokyo and retired in 2018. Then he moved to Meiji University, a private university in Tokyo. He is mainly interested in propagation phenomena in various mathematical models

The project

Title: Front propagation through heterogeneous media and its applications

"This project is concerned with front propagation in reaction-diffusion equations. Reaction-diffusion models are used in a variety of disciplines, such as ecology, physiology, chemical engineering, sociology and anthropology. In this project, we study front propagation, namely the motion of a wave front that propagates in space. Front propagation can be found in various fields of sciences. An important example in ecology is the biological invasion by alien species into new habitat. In this case the front represents the territorial boundary of the invading species. Reaction-diffusion models also appear in the study of problems in sociology (e.g. spreading of crimes) and anthropology (e.g. spreading of farming during the Neolithic era). In the project in 2024, we plan to further develop the above research. Among other things we will consider the case where the holes are arrayed non-periodically on the wall and discuss whether the front can penetrate the wall or not. We will also consider the case where the wall is replaced by a perforated zone of infinite thickness. We also plan to explore applications of this mathematical research to such fields as ecology and sociology."

Hosting institution: École des Hautes Études et Sciences Sociales (EHESS)

Selective Bibliography

• H. Matano, Y. Mori, and M. Nara, Stability of front solutions of the bidomain Allen-Cahn equation on an infinite strip, SIAM J. Math. Anal. 55 (3) (2023).  
• D. Hilhorst, H. Matano, T.N. Nguyen and H. Weber, Generation of interface for solutions of the mass conserved Allen-Cahn equation, SIAM J. Math. Anal. 52 (3) (2020), pp. 2624-2654.  
• A. Ducrot, T. Giletti and H. Matano, Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type, Calc. Var. Partial Differential Equations 58 (4) (2019). doi: 10.1007/s00526-019-1576-2
• H. Matano, Y. Mori and M. Nara, Asymptotic behavior of spreading fronts in the anisotropic Allen–Cahn equation on R^n, Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36 (3) (2019), pp. 585--626.