Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/8920
Title: The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line
Authors: Özsarı, Türker
Yolcu, Nermin
Keywords: Schrodinger equation
Biharmonic Schrodinger equation
Fokas method
Unified transform method
Local wellposedness
Space estimates
Strichartz estimates
Inhomogeneous boundary data
Issue Date: 2019
Publisher: American Institute of Mathematical Sciences
Abstract: We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schrodinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for the solution of the linear nonhomogenenous problem by using the Fokas method (also known as the unified transform method). We use this representation formula to prove space and time estimates on the solutions of the linear model in fractional Sobolev spaces by using Fourier analysis. Secondly, we consider the nonlinear model with a power type nonlinearity and prove the local wellposedness by means of a classical contraction argument. We obtain Strichartz estimates to treat the low regularity case by using the oscillatory integral theory directly on the representation formula provided by the Fokas method. Global wellposedness of the defocusing model is established up to cubic nonlinearities by using the multiplier technique and proving hidden trace regularities.
URI: https://doi.org/10.3934/cpaa.2019148
https://hdl.handle.net/11147/8920
ISSN: 1534-0392
1553-5258
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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