研究テーマ:

偏微分方程式（PDE）の理論的研究を行っています. PDEの中でも特に分散型と呼ばれる分類の方程式（Schrödinger方程式など）に興味を持っており, それに関連する非線形問題の解析が主な研究課題です. 

キーワード:　(分散型非線形偏微分方程式,  Schrödinger写像, Laudau-Lifshitz方程式)

論文:

[1] I. Shimizu, Remarks on local theory for Schrödinger maps near harmonic maps, Kodai Math. J. 43 (2020), 278-324. [arXiv]

[2] I. Shimizu, On uniqueness for Schrödinger maps with low regularity large data, Differential Integral Equations 33 (2020), 207-222. [arXiv], [errata]

[3] I. Shimizu, Local well-posedness of the Landau-Lifshitz equation with helicity term, J. Math. Phys. 63 (2022), 091505. [arXiv]

[4] S. Ibrahim and I. Shimizu, Phase transition threshold and stability of magnetic skyrmions, Commun. Math. Phys. 402  (2023) no. 3, 2627--2640. [arXiv]

[5] M. Ikeda, T. Inui, M. Hamano, and I. Shimizu, Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph, Partial Diffe. Equ. Appl. 5 (2024) no. 5, Paper No. 4. [arXiv]

[6] S. Gustafson, T. Inui, and I. Shimizu, Multi-solitons for the nonlinear Schrödinger equation with repulsive Dirac delta potential, Nonlinear Differential Equations and Applications NoDEA 32 (2025) no. 3, Article No. 53. [arXiv]

[7] M. Ishiwata and I. Shimizu, A remark on the long-time asymptotics of global-in-time solutions for semilinear parabolic equations in $\mathbb{R}^N$, Canad. J. Math. (Published online)

[8] M. Ikeda, T. Inui, M. Hamano, and I. Shimizu, A note on global dynamics for nonlinear Schrödinger equations on star graphs, RIMS Kôkyûroku Bessatsu B97 (2025), 037--052.

[9] S. Ibrahim and I. Shimizu, Global perturbation of isolated equivariant chiral skyrmions from the harmonic maps, preprint. [arXiv:2503.03209]

[10] S. Ibrahim, T. Miura, C. Roman, and I. Shimizu, Phase transition threholds and chiral magnetic fields of general degree, preprint. [arXiv:2512.24598]

[11] I. Shimizu, Time decay estimates for localized perturbations around a helical state for the Landau-Lifshitz-Gilbert equation, preprint. [arXiv:2601.17941]