Inhomogeneous dirichlet–boundary value problem for two-dimensional quadratic nonlinear schrÖdinger equations

Nakao Hayashi; Elena I. Kaikina

doi:10.2206/kyushujm.74.375

Inhomogeneous dirichlet–boundary value problem for two-dimensional quadratic nonlinear schrÖdinger equations

Nakao Hayashi, Elena I. Kaikina

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.

Original language	English
Pages (from-to)	375-400
Number of pages	26
Journal	Kyushu Journal of Mathematics
Volume	74
Issue number	2
DOIs	https://doi.org/10.2206/kyushujm.74.375
Publication status	Published - 2020
Externally published	Yes

Keywords

Inhomogeneous initial–boundary value problem
Large-time asymptotics
Nonlinear Schrödinger equation
Upper half-plane

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.74.375

Cite this

@article{3b18b49125a14644bebe510191b62306,

title = "Inhomogeneous dirichlet–boundary value problem for two-dimensional quadratic nonlinear schr{\"O}dinger equations",

abstract = "We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schr{\"o}dinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schr{\"o}dinger group.",

keywords = "Inhomogeneous initial–boundary value problem, Large-time asymptotics, Nonlinear Schr{\"o}dinger equation, Upper half-plane",

author = "Nakao Hayashi and Kaikina, {Elena I.}",

note = "Funding Information: We would like to thank the unknown referee for his/her useful comments on the first draft. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP19H05597, JP15H03630. The work of E.I.K. is partially supported by CONACYT 252053-F and PAPIIT project IN100817. Publisher Copyright: {\textcopyright} 2020 Faculty of Mathematics, Kyushu University.",

year = "2020",

doi = "10.2206/kyushujm.74.375",

language = "English",

volume = "74",

pages = "375--400",

journal = "Kyushu Journal of Mathematics",

issn = "1340-6116",

publisher = "Kyushu University, Faculty of Science",

number = "2",

}

TY - JOUR

T1 - Inhomogeneous dirichlet–boundary value problem for two-dimensional quadratic nonlinear schrÖdinger equations

AU - Hayashi, Nakao

AU - Kaikina, Elena I.

N1 - Funding Information: We would like to thank the unknown referee for his/her useful comments on the first draft. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP19H05597, JP15H03630. The work of E.I.K. is partially supported by CONACYT 252053-F and PAPIIT project IN100817. Publisher Copyright: © 2020 Faculty of Mathematics, Kyushu University.

PY - 2020

Y1 - 2020

N2 - We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.

AB - We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.

KW - Inhomogeneous initial–boundary value problem

KW - Large-time asymptotics

KW - Nonlinear Schrödinger equation

KW - Upper half-plane

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DO - 10.2206/kyushujm.74.375

M3 - Article

AN - SCOPUS:85097926002

SN - 1340-6116

VL - 74

SP - 375

EP - 400

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

IS - 2

ER -

Inhomogeneous dirichlet–boundary value problem for two-dimensional quadratic nonlinear schrÖdinger equations

Abstract

Keywords

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