The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane

This work studies the initial-boundary value problem (ibvp) of the two-dimensional nonlinear Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It establishes well-posedness in the sense of Hadamard by using t...

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Veröffentlicht in:	Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2022-09, Vol.478 (2265)
Hauptverfasser:	Alexandrou Himonas, A., Mantzavinos, Dionyssios
Format:	Artikel
Sprache:	eng
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container_title	Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences
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creator	Alexandrou Himonas, A. Mantzavinos, Dionyssios
description	This work studies the initial-boundary value problem (ibvp) of the two-dimensional nonlinear Schrödinger equation on the half-plane with initial data in Sobolev spaces and Neumann or Robin boundary data in appropriate Bourgain spaces. It establishes well-posedness in the sense of Hadamard by using the explicit solution formula for the forced linear ibvp obtained via Fokas’s unified transform, and a contraction mapping argument.
doi_str_mv	10.1098/rspa.2022.0279
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title	The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane
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