Mathematical Analysis of Models
Staff
Research Topics
We are working on applied mathematical analysis and its application to mathematical models of natural phenomena. The mathematical models are described in terms of functional equations (ordinary differential equations, delay differential equations, partial differential equations). The application covers wide range of studies, such as biology and geophysics.
Applied Analysis
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This subject concerns properties of solutions to functional equations, such as ordinary differential equations, delay differential equations and partial differential equations. Besides mathematical arguments, numerical analysis and symbolic computation are also employed as needed. |
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Biomathematics
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This subject concerns problems in biology and life science, which are considered with mathematical models. The subject also concerns mathematical methods that can be applied to problems in biology and life science. For example, problems in ecology, epidemics and virus dynamics are considered. |
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Numerical analysis of two-dimansional turbulence on a rapidly rotatting sphere
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Two-dimensional barotropic flow described by the two-dimensional Navier-Stokes equation on a rotating sphere is one the simplest mathematical models for planetary atmospheres. Flow fields of this system show spontaneous large-scale zonal-flow formation, like stripe structures observed on giant planets. I am trying to clarify the mechanism of this large-scale zonal-flow structure formation. |
 Emergence and the temporal development of large-scale zoanl flows in two-dimensional turbulence on a rotating sphere. |
Research on feature formation in organisms with unique and highly functional features
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Some organisms possess highly unique body structures and biological properties. In order to obtain knowledge, information, and good understandings of essential factors related to the appearance and formation of such characteristic features, I am performing two different kinds of investigations. One is bioinformatics-based data analysis of genetic and some biological data obtained by experiments, and the other is based on mathematical modellings and numerical simulations. |
 Nanometre-order pores regularly arranged in diatom shells |
Publication List
- Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani, Global stability of an age-structured multistrain virus dynamics model with humoral immunity, J. Appl. Math. 62-1-2 (2020) 239-279
- Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani, Global stability of an age-structured model for pathogen-immune interaction, J. Appl. Math. Comput., 59-1-2 (2019) 631-660
- Toru Sasaki, Takashi Suzuki, Asymptotic behaviour of the solution to a virus dynamics model with diffusion, Discrete Contin. Dyn. Syst. Ser. B, 23(2) (2018) 525-541
- Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki, Lyapunov functionals for multistrain models with infinite delay, Discrete Contin. Dyn. Syst. Ser. B, 22-2 (2017) 507-536
- Tsuyoshi Kajiwara, Toru Sasaki, and Yasuhiro Takeuchi, Construction of Lyapunov functions for some models of infectious deseases in vivo: from simple models to complex models, Mathematical Biosciences and Engineering 12-1 (2015) 117--133
- M.Nemoto, S.Iwaki, H.Moriya, Y. Monden, T. Tamura, K.Inagaki, S. Mayama, and K.Obuse, “Comparative gene analysis focused on silica cell wall formation: Identification of diatom-specific SET domain protein methyltransferases”, Mar. Biotech. 22(4), 551-563, (2020)
- K. Obuse and M. Yamada, “Energy Transfer to Resonant Zonal Rossby Modes in Two-Dimensional Turbulence on a Rotating Sphere”, J. Phys. Soc. Jpn., 89(6), (2020) 064401
- K. Obuse and M. Yamada, “Three-wave resonant interactions and zonal flows in two-dimensional Rossby--Haurwitz wave turbulence on a rotating sphere”, Phys. Rev. Fluids 4, (2019) 024601
- Kiori Obuse, Shin-ichi Takehiro, and Michio Yamada, “Linear stability of steady zonal jet flows induced by a small-scale forcing on a βplane”, Physica D, 240, (2011), 1825-1834
- Kiori Obuse, Shin-ichi Takehiro and Michio Yamada, “Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere”, Physics of Fluids, 22(5), (2010), 1-9 056601