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成果
随時更新いたします。
H. Kodani, K. Matsue, H. Ochiai, and A. Takayasu, Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. II -- Dynamical Correspondence, Nonlinearity, Vol. 38, No. 4, 045004, 41 pages, March 2025. ( https://doi.org/10.1088/1361-6544/adb52e )
T. Asai, H. Kodani, K. Matsue, H. Ochiai and T. Sasaki, "Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I - Method and Justification", Vol. 38, No. 4, 045003, 52 pages, March 2025. ( https://iopscience.iop.org/article/10.1088/1361-6544/adb52d )
G. W. Duchesne, J.-P. Lessard, and A. Takayasu, A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory, J. Sci. Comput., Vol. 102, 62, 66 pages, January 2025. ( https://doi.org/10.1007/s10915-024-02785-x )
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K. Anada, T. Ishiwata and T. Ushijima, Type II singularities in area-preserving curvature flows of convex symmetric immersed closed plane curves, Journal of Differential Equations, Vol. 437, 17 pages, April 2025. ( https://doi.org/10.1016/j.jde.2025.113348 )
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Kaname Matsue, "Blow-up behavior for ODEs with normally hyperbolic nature in dynamics at infinity", SIAM Journal on Applied Dynamical Systems, 24(2025), 415-456. ( https://epubs.siam.org/doi/full/10.1137/23M1588561 )
(解説記事) 松江 要、"微分方程式・数値解析に現れる不動点定理とその展開", 数理科学@サイエンス社, (2024) 8月号
K. Anada, T. Ishiwata and T. Ushijima, "Upper Estimates for Blow-up Solutions of a Quasi-Linear Parabolic Equation", Japan Journal of Industrial and Applied Mathematics, Vol. 41, 381--405, 2024. ( https://link.springer.com/article/10.1007/s13160-023-00606-6 )
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Jean-Philippe Lessard, Kaname Matsue & Akitoshi Takayasu, "Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature", Journal of Nonlinear Science, March 2023.
( https://link.springer.com/article/10.1007/s00332-023-09900-6 )
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Tetsuya Ishiwata and Yukihiko Nakata, A note on blow-up solutions for a scalar differential equation with a discrete delay, Japan Journal of Industrial and Applied Mathematics, Vol. 39, 959--972, 2022. (doi:10.1007/s13160-022-00533-y)
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Koichi Anada, Tetsuya Ishiwata and Takeo Ushijima, Asymptotic Expansions of Traveling Wave Solutions for a Quasilinear Parabolic Equation, Japan Journal of Industrial and Applied Mathematics, Vol. 39, 889--920, 2022. (doi:10.1007/s13160-022-00532-z)
Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette & Hisashi Okamoto, "Rigorous numerics for nonlinear heat equations in the complex plane of time", Numerische Mathematik, Vol. 151, 693--750, July 2022. ( https://doi.org/10.1007/s00211-022-01291-2 )
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Jonathan Jaquette, Jean-Philippe Lessard & Akitoshi Takayasu, "Global dynamics in nonconservative nonlinear Schrödinger equations", Advances in Mathematics, Vol. 398, 108234, 70 pages, March 2022. ( https://doi.org/10.1016/j.aim.2022.108234 )
Jonathan Jaquette, Jean-Philippe Lessard & Akitoshi Takayasu, "Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity", Communications in Nonlinear Science and Numerical Simulation, Vol. 107, 106188, 14 pages, April 2022. ( https://doi.org/10.1016/j.cnsns.2021.106188 )
Alexey Eremin, Emiko Ishiwata, Tetsuya Ishiwata & Yukihiko Nakata, "Delay-induced blow-up in a planar oscillation model", Japan Journal of Industrial and Applied Mathematics (2021), https://link.springer.com/content/pdf/10.1007/s13160-021-00475-x.pdf
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Kaname Matsue, "A simple description of blow-up solutions through dynamics at infinity in nonautonomous ODEs", arXiv:2504.02718 https://arxiv.org/abs/2504.02718
M. Cadiot, J. Jaquette, J.-P. Lessard, and A. Takayasu, "Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs", arXiv:2411.18361, https://arxiv.org/abs/2411.18361
T. Ishige and A. Takayasu, "Computer-assisted proofs for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces", arXiv:2501.03792, https://arxiv.org/abs/2501.03792
本課題の基礎となった論文のリストです。
Y. Ichida, K. Matsue and T.O. Sakamoto, "A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations", JSIAM Lett., 12(2020), 65-68.
( https://www.jstage.jst.go.jp/article/jsiaml/12/0/12_65/_article/-char/ja/ )
K. Matsue, "On blow-up solutions of differential equations with Poincare-type compactifications", SIAM J. Appl. Dyn. Sys., 17(2018), 2249-2288.
( https://epubs.siam.org/doi/10.1137/17M1124498 )
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松江 要, "サドル", 数学セミナー, 58(2019), 12月号
K. Matsue, "Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs", J. Diff. Eq., 267(2019), 7313-7368.
( https://www.sciencedirect.com/science/article/pii/S0022039619303274 )
K. Matsue and A. Takayasu, "Numerical validation of blow-up solutions with quasi-homogeneous compactifications", Numerische Mathematik, 145(3) (2020), 605-654.
( https://link.springer.com/article/10.1007/s00211-020-01125-z )
K. Matsue and A. Takayasu, "Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity", J. Comput. Appl. Math., 374(2020), 112607.
( https://www.sciencedirect.com/science/article/pii/S0377042719306120 )
松江 要, "微分方程式の爆発解：精度保証付き数値計算と力学系的解釈 ", 日本シミュレーション学会誌「シミュレーション」, 37(2018)
A. Takayasu, K. Matsue, T. Sasaki, K. Tanaka, M. Mizuguchi and S. Oishi, "Numerical validation of blow-up solutions for ODEs", J. Comp. Appl. Math., 314(2017), 10-29.
( https://www.sciencedirect.com/science/article/pii/S0377042716305027 )
M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi, "A method of verified computations for solutions to semilinear parabolic equations using semigroup theory", SIAM J. Numer. Anal., 55:2(2017), 980-1001.
M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi, "Numerical verification for existence of a global-in-time solution to semilinear parabolic equations", J. Comput. Appl. Math., 315(2017), 1-16.
A. Takayasu, S. Yoon and Y. Endo, "Rigorous numerical computations for 1D advection equations with variable coefficients", Japan J. Ind. Appl. Math., 36(2019), 357-384.
T. Ishiwata and S. Yazaki, "A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion", Discrete and Continuous Dynamical Systems Ser. A 34 (2014), No. 5, 2069--2090.
K. Anada and T. Ishiwata, "Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation", J. Diff. Eq., 262(2017), 181–271.
T. Ishiwata and Y.C. Yang, "Numerical and mathematical analysis of blow-up problems for a stochastic differential equation", Discrete and Continuous Dynamical Systems Ser. S., doi:10.3934/dcdss.2020391
T. Ishiwata and T. Sasaki, "The blow-up curve of solutions to one dimensional nonlinear wave equations with the Dirichlet boundary conditions", Japan Journal of Industrial and Applied Mathematics, 37(2020), 339-363.
本課題以外にも、事業者は幅広い研究分野にて研究活動の成果を発表しています。
そのような成果（出版物、プレプリント含む）をここにまとめています。ご参考までに。
(プレプリント) Kaname Matsue and Kyoko Tomoeda, "Particle-Laden Flows on Non-Flat Inclines in the Settled Regime: Mathematical Modeling and Numerical Investigations", preprint and submitted.
(プレプリント) Takashi Kagaya, Miyuki Koiso and Kaname Matsue, "Continuation of Capillary Surfaces with Topological Change via the Van Der Waals-Cahn-Hilliard Theory", preprint and submitted.
(プレプリント) Dinh Hoa Nguyen and Kaname Matsue, "Characterization of Maximizers in A Non-Convex Geometric Optimization Problem With Application to Optical Wireless Power Transfer Systems", arXiv:2404.13832 https://arxiv.org/abs/2404.13832
(論文) Chiang-Mei Chen, Toshimasa Ishige, Sang Pyo Kim, Akitoshi Takayasu, and Chun-Yu Wei, "Monodromy Approach to Pair Production of Charged Black Holes and Electric Fields", Chinese Journal of Physics, Vol. 86, pp. 255-268, December 2023. (https://doi.org/10.1016/j.cjph.2023.10.007)
(論文) Kaname Matsue and Moshe Matalon, "Dynamics of hydrodynamically unstable premixed flames in a gravitational field - Local and global bifurcation structures", Combustion Theory and Modelling (2023) https://www.tandfonline.com/doi/full/10.1080/13647830.2023.2165968
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(論文) Kaname Matsue and Kyoko Tomoeda, "A mathematical treatment of the bump structure of the particle-laden flows with particle features", arXiv:2105.07389, https://arxiv.org/abs/2105.07389, Japan Journal of Industrial and Applied Mathematics (2022), https://link.springer.com/article/10.1007/s13160-022-00521-2
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(論文) Koki Nitta, Nobito Yamamoto and Kaname Matsue, "A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions", Japan Journal of Industrial and Applied Mathematics (2022), https://link.springer.com/article/10.1007/s13160-022-00502-5
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(書籍) 岡本 健太郎, 松江 要 (著), 国立研究開発法人科学技術振興機構研究開発戦略センター(JST/CRDS), 高島 洋典, 吉脇 理雄 (編集), 「社会に最先端の数学が求められるワケ (1) 新しい数学と産業の協奏」, 日本評論社, 2022年3月30日
(2巻も同時発売, 座談会に松江が出演)
(論文) K. Kuwana, K. Matsue, Y. Fukumoto, R. Dobashi and K. Saito, "Fire whirls: A Combustion Science Perspective", Combustion Science and Technology (2022), https://doi.org/10.1080/00102202.2021.2019234
(論文) A. Imakura, K. Morikuni, & A. Takayasu, "Complex moment-based methods for differential eigenvalue problems", Numer. Algor., 92, 693-721, January 2023. ( https://doi.org/10.1007/s11075-022-01456-y )
(論文) A. Imakura, K. Morikuni, & A. Takayasu, "Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems", J. Comput. Appl. Math., Vol. 424, 114994, 18 pages, May 2023. ( https://doi.org/10.1016/j.cam.2022.114994 )
(論文) A. Imakura, K. Morikuni & A. Takayasu, "Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems", J. Comput. Appl. Math., Vol. 369, 112543, 11 pages, May 2020. ( https://doi.org/10.1016/j.cam.2019.112543 )