Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations

@inproceedings{Bona2018NonhomogeneousBP,
  title={Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schr{\"o}dinger equations},
  author={Jerry L. Bona and Shu-Ming Sun and Bing-Yu Zhang},
  year={2018}
}
This paper is concerned with initial-boundary-value problems (IBVPs) for a class of nonlinear Schrödinger equations posed either on a half line R or on a bounded interval (0, L) with nonhomogeneous boundary conditions. For any s with 0 ≤ s < 5/2 and s 6= 3/2, it is shown that the relevant IBVPs are locally well-posed if the initial data lie in the L– based Sobolev spaces H(R) in the case of the half line and in H(0, L) on a bounded interval, provided the boundary data are selected from H (2s+1… CONTINUE READING

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