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USAMI Hiroyuki
Title Professor
Department Department of Electrical, Electronic and Computer Engineering
Course Applied Physics Course

Research fields

The main theme of our research is to find asymptotic properties of solutions of various types of differential equations, that is, we want to know what properties the solutions under consideration show when the independent variables go to the infinty. From the physical point of view, It can be said that we want to know what the ultimate situations of the phenomena described by the differential equations are.

Since not all differential equations can be solved explicitly, it is one of the most important problems to analyse differential equations rigorously.

In particular, we are interested in the following equations:
・Nonlinear ordinary differential equations with time varying coefficients. The study of equations listed below are sometimes based on the results obtained from the analysis of such equations;
・Ordinary differential systems appearing in biology, economics and so on, such as Lotka-Volterra systems and Lanchester-type models ;
・Elliptic partial differential equatioins, which often used to describe stationary problems;
・Hyperbolic partial equations, which often used to describe vibration phenomena;
・Differential equations with deviating arguments; more precisely, delay differential equations.

Research Keywords

differential equation asymptotic behavior qualitative theory

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