Well-posedness and Large time behavior of solutions to Nonlinear Dispersive Equations
非線型分散型偏微分方程式における解の適切性と時間大域挙動の解明
Hayato Miyazaki and Motohiro Sobajima, Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance, Published electronically in Proceedings of the American Mathematical Society. [Link | arXiv]
Naoyasu Kita, Hayato Miyazaki and Takuya Sato, Refinement of the $L^{2}$-decay estimate of solutions to nonlinear Schrödinger equations with attractive-dissipative nonlinearity, Journal of Evolution Equations, 25, 66 (2025). [Link | arXiv]
Masaki Kawamoto, Satoshi Masaki and Hayato Miyazaki, Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance, Mathematische Annalen 392, 1051-1097 (2025). [Link | arXiv]
Masaki Kawamoto and Hayato Miyazaki, Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials, Nonlinear Analysis, Volume 256, July 2025, 113778. [Link | arXiv]
Naoyasu Kita, Hayato Miyazaki, Yuji Sagawa, Takuya Sato, Refined $L^2$-decay estimate of solutions to a system of dissipative nonlinear Schrödinger equations, Journal of Applied Science and Engineering A, Volume 5, Issue 1, 2024, pp.18-30. [Link]
Satoshi Masaki and Hayato Miyazaki, Global behavior of solutions to generalized Gross-Pitaevskii equation, Differential Equations and Dynamical Systems 32, 743-761 (2024). [Link | arXiv]
Masaki Kawamoto and Hayato Miyazaki, Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials, Journal of Differential Equations 365 (2023) 127-167. [Link | arXiv]
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani and Kota Uriya, Asymptotic behavior for the long-range nonlinear Schrödinger equation on star graph with the Kirchhoff boundary condition, Pure and Applied Analysis 4-2 (2022), 287-311. [Link | arXiv]
Hayato Miyazaki, Local well-posedness for the higher-order generalized KdV type equation with low-degree of nonlinearity, to appear in RIMS Kôkyûroku Bessatsu. [arXiv]
Hayato Miyazaki, Strong blow-up instability for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations, Discrete & Continuous Dynamical Systems, 41 (2021), no. 5, 2411-2445. [Link | arXiv]
Hayato Miyazaki and Motohiro Sobajima, Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order, Advances in Harmonic Analysis and Partial Differential Equations (2020), pp. 197-207. [Link | arXiv]
Hayato Miyazaki, Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity, Advanced Studies in Pure Mathematics 85 (2020), The Role of Metrics in the Theory of Partial Differential Equations, pp. 303-313. [Link]
Felipe Linares, Hayato Miyazaki and Gustavo Ponce, On a class of solutions to the generalized KdV type equation, Communications in Contemporary Mathematics 21 (2019), no.7, 1850056, 21 pp. [Link | arXiv]
Satoshi Masaki, Hayato Miyazaki and Kota Uriya, Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity in three space dimensions, Transactions of the American Mathematical Society 371 (2019), no. 11, 7925-7947. [Link | arXiv]
Satoshi Masaki and Hayato Miyazaki, Nonexistence of scattering and modified scattering states for some nonlinear Schrödinger equation with critical homogeneous nonlinearity, Differential and Integral Equations 32 (2019), no. 3-4, 121-138. [Link | arXiv]
Satoshi Masaki and Hayato Miyazaki, Long range scattering for nonlinear Schrödinger equations with critical homogeneous nonlinearity, SIAM Journal on Mathematical Analysis 50 (2018), no. 3, 3251–3270. [Link | arXiv]
Kazumasa Fujiwara and Hayato Miyazaki, The derivation of conservation laws for nonlinear Schrödinger equations with power type nonlinearities, RIMS Kôkyûroku Bessatsu B63 (2017), 13-21. [Link] (Previous version [arXiv])
Hayato Miyazaki, The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity, Journal of Mathematical Analysis and Applications 417 (2014), no. 2 580-600. [Link | arXiv]
Kazuki Aoki, Takahisa Inui, Hayato Miyazaki, Haruya Mizutani and Kota Uriya, Modified scattering for inhomogeneous nonlinear Schrödinger equations with and without inverse-square potential, submitted. [arXiv]
宮﨑隼人, Kirchhoff境界条件を持つ星グラフ上のSchrödinger作用素について, RIMS Kôkyûroku, No.2324 (in Japanese). [Link]
Hayato Miyazaki, Improvement of a regularity condition for long-range scattering for NLS with critical homogeneous nonlinearity, RIMS Kôkyûroku, No.2257. [Link]
宮﨑隼人, 空間遠方で消滅しない境界条件をもつ非線型シュレディンガー方程式のエネルギー解について, 第36回発展方程式若手セミナー報告集, 2014年12月, p175-182 (in Japanese).
宮﨑隼人, 空間遠方で消滅しない初期値をもつ非線形Schrödinger方程式における保存則について, 第35回発展方程式若手セミナー報告集, 2013年12月, p79-84 (in Japanese).
2025/06/26 (Invited) East-Asian workshop on dispersive equations
Venue: Kensington Resort Seogwipo, South Korea
Title: $L^{2}$-decay of solutions to nonlinear Schrödinger equations with attractive-dissipative nonlinearity
2024/10/29 (Invited) RIMS Symposia (open) Evolution Equations and Related Topics -Quantitative Analysis and Abstract Structures-
Venue: Maskawa Hall, Kyoto Univerisity
Title: Global well-posedness for NLS without gauge-invariance below the Strauss exponent
2024/08/22 (Invited) Imadegawa Workshop on Dispersive Equations
Venue: RYB1, Basement 1, Ryoshinkan, Doshisha University
Title: Global well-posedness for NLS without gauge-invariance below the Strauss exponent
2024/05/08 (Invited) PDEs Research Group Seminar
Venue: Online (University of Nottingham Ningbo China)
Title: Modified scattering operator for nonlinear Schrödinger equations with a time-decaying harmonic potential
2024/04/25 (Invited) Workshop on dispersive PDE
Venue: S1-1, 450, Chungbuk National University, Cheongju, South Korea
Title: Modified scattering operator for nonlinear Schrödinger equations with a time-decaying harmonic potential
2024/02/22 (Invited) Colloquium
Venue: Room 3174, Department of Mathematics, National Cheng Kung University, Taiwan
Title: Modified scattering operator for nonlinear Schrödinger equations with a time-decaying harmonic potential
2022/12/02 (Invited) RIMS Symposia (open) Spectral and Scattering Theory and Related Topics
Venue: Room No. 111, RIMS, Kyoto University
Title: Long-range scattering for a homogeneous type nonlinear Schrödinger equation
2022/03/03 (Invited) Himeji Conference on Partial Differential Equations 2022
Venue: Online
Title: Long-range scattering for a homogeneous type nonlinear Schrödinger equation
2021/09/10 (Invited) California State University, Fullerton Geometry Seminar
Venue: Online
Title: Asymptotic behavior of solutions to the long-range nonlinear Schrödinger equation on a star graph
2019/08/01 (Invited) 12th International ISAAC Congress, Session : Harmonic Analysis and Partial Differential Equations
Venue: Room 23.1.5, University of Aveiro, Portugal
Title: Strong instability for standing wave solutions to the system of the quadratic NLKG
2018/07/19 (Invited) International Workshop on “Fundamental Problems in Mathematical and Theoretical Physics”
Venue: Bldg. #55-N, Nishi-Waseda Campus, Waseda University
Title: The initial value problem for the generalized KdV equation with low degree of non-linearity
2018/07/06 (Invited) The 11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI) The Role of Metrics in the Theory of Partial Differential Equations
Venue: Conference Room 1, Hokkaido University
Title: The initial value problem for the generalized KdV equation with low degree of non-linearity
2017/11/17 (Invited) UCSB Applied/PDE seminar
Venue: South Hall 4607, University of California, Santa Barbara, USA
Title: Long time behavior of solutions to the nonlinear Schrödinger equation with critical homogeneous nonlinearity
2017/03/13 (Invited) Workshop on nonlinear dispersive equations in Osaka, 2017
Venue: Graduate School of Engineering Science Bldg. J-617, Osaka University
Title: Long range scattering for NLS equation with critical homogeneous nonlinearity I
2016/08/24 (Poster Session) Mathematical Analysis for Stability in Nonlinear Dynamics -in honor of Professor Vladimir Georgiev on his 60th birthday-
Venue: 7-310 & 7-219/220, Faculty of Science Bld. #7, Hokkaido University
Title: Global behavior of solutions to Generalized Gross-Pitaevskii equation
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