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Organization for Research Development and Outreach, Research Support Center
- Professor
- Yoshihiro HAMAYA
- Research Field
Qualitative theory of functional difference equations and functional differential equations
- Keyword(s)
Stability property, Periodic solutions, Almost periodic solutions, Liapunov functions
- Research theme
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- We study to make existence theorems of family of almost periodic solutions to functional difference/differential equations.
- We have the application of functional difference/differential equations to the model of mathematical ecology.
- We consider the application of functional difference/differential equations to mathematical somatology, mathematical biology, mathematical sociology and etc.
Outline of research activitiesMy recent research activity is to find sufficient conditions for global asymptotic stability of equilibrium solutions of delayed partial differential equations with diffusion. An application is the SIR or SEIR epidemic model, which visualizes the results obtained in general theory using a computer (SDGs03). In addation, we have main study to search the sufficient condition which is equivalent to some kind of weakly asymptotically stable, in order to obtain the existence theorem and property of the family of almost periodic solutions to the functional difference equations with time delay. For this example, we construct a model of the erectile dysfunction by the radiational minimal explosion and by analyzing this model, and also we are studying the condition of coefficient on functional difference equations to adapt the real case of erectile dysfunction. Moreover, we verify from aspect of the sex medicine that this constructed model well explains a family of almost periodic system which appears the case of the erectile dysfunction by the radiation minimal explosion whether or not, by cooperating with a team of the department of urology in Kawasaki Medical University (SDGs03,SDGs15).
- Desired cooperation
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- Qualitative theory of functional difference/differential equations, descrete dynamics, mathematical somatology, mathematical biology, mathematical sociology, functional erectile dysfunctions