Abstract
We consider the inhomogeneous Dirichlet-boundary value problem with large initial and boundary data for nonlinear Schrödinger equations in one space dimension. Global existence and asymptotic behavior in time of solutions to the problem are obtained by using the classical energy method and factorization techniques.
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Acknowledgements
The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP25220702, JP15H03630. The work of E.I.K. is partially supported by CONACYT 252053-F and PAPIIT project IN100817. The work of T.O. is partially supported by JSPS KAKENHI Grant Number JP25220702.
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Hayashi, N., Kaikina, E.I. & Ogawa, T. Dirichlet-boundary value problem for one dimensional nonlinear Schrödinger equations with large initial and boundary data. Nonlinear Differ. Equ. Appl. 27, 17 (2020). https://doi.org/10.1007/s00030-020-0618-y
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DOI: https://doi.org/10.1007/s00030-020-0618-y
Keywords
- Nonlinear Schrödinger equation
- Large time asymptotics
- Inhomogeneous initial-boundary value problem
- Large data