Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Sunagawa, Hideaki"'
We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.
Comment: 15 pages. arXiv admin note: text overlap with arXiv:2204.07320
Comment: 15 pages. arXiv admin note: text overlap with arXiv:2204.07320
Externí odkaz:
http://arxiv.org/abs/2303.17801
Publikováno v:
Discrete Contin. Dyn. Syst., 2022, Volume 42, Issue 12: 5893-5908
We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as $t\to +\inf
Externí odkaz:
http://arxiv.org/abs/2204.07320
Publikováno v:
J. Evol. Equ. 21 (2021), no. 2, 1541-1550
We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equation in one space dimension. Under a suitable weakly dissipative condition on the nonlinearity, we show that the small data solution has a logarithmic time decay i
Externí odkaz:
http://arxiv.org/abs/2004.12075
Publikováno v:
J. Math. Soc. Japan 73 (2021), no.3, 767-779
This article gives an energy decay result for small data solutions to a class of semilinear wave equations in two space dimensions possessing weakly dissipative structure relevant to the Agemi condition.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2002.09639
Publikováno v:
Tokyo J. Math. 44 (2) 411 - 416, December 2021
This is a sequel to the paper "Large time asymptotics for a cubic nonlinear Schr\"odinger system in one space dimension" by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schr\"odinger equati
Externí odkaz:
http://arxiv.org/abs/2001.10682
Publikováno v:
Funkcialaj Ekvacioj, 2021 Volume 64, Issue 3, Pages 361-377
We consider a two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong restriction betwee
Externí odkaz:
http://arxiv.org/abs/1905.07123
Autor:
Nishii, Yoshinori, Sunagawa, Hideaki
Publikováno v:
Journal of Hyperbolic Differential Equations, vol.17 (2020), no.3, p.459-473
We consider a two-component system of cubic semilinear wave equations in two space dimensions satisfying the Agemi-type structural condition (Ag) but violating (Ag$_0$) and (Ag$_+$). For this system, we show that small amplitude solutions are asympto
Externí odkaz:
http://arxiv.org/abs/1904.09083
Autor:
Sakoda, Daisuke, Sunagawa, Hideaki
Publikováno v:
Journal of Differential Equations, vol.268 (2020), p.1722 -- 1749
This paper provides a small data global existence result for a class of quadratic derivative nonlinear Schr\"odinger systems in two space dimensions. This is an extension of the previous results by Li [Discrete Contin. Dyn. Syst., 32 (2012), 4265--42
Externí odkaz:
http://arxiv.org/abs/1804.05540
Let $T_{\epsilon}$ be the lifespan for the solution to the Schr\"odinger equation on $\mathbb{R}^d$ with a power nonlinearity $\lambda |u|^{2\theta/d}u$ ($\lambda \in \mathbb{C}$, $0<\theta<1$) and the initial data in the form $\epsilon \varphi(x)$.
Externí odkaz:
http://arxiv.org/abs/1703.03125
Autor:
Li, Chunhua, Sunagawa, Hideaki
Publikováno v:
Advanced Studies in Pure Mathematics, vol.81 (2019), p.173 - 195
We prove global existence of small solutions to the initial value problem for a class of cubic derivative nonlinear Schr\"odinger systems with the masses satisfying suitable non-resonance relations. The large-time asymptotics of the solutions are als
Externí odkaz:
http://arxiv.org/abs/1603.04966