On the non-homogeneous boundary value problem for Schrödinger equations

DOI10.3934/dcds.2013.33.3861zbMath1285.35104OpenAlexW2323421853MaRDI QIDQ379541

Corentin Audiard

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2013.33.3861

zbMATH Keywords

Schrödinger equationslocal smoothingdispersive estimatesconvex obstaclesnon-homogeneous boundary value problemnon-trapping obstacles

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Nonhomogeneous Boundary Value Problems of Nonlinear Schrödinger Equations in a Half Plane ⋮ Avoiding order reduction when integrating nonlinear Schrödinger equation with Strang method ⋮ Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations ⋮ Complex Ginzburg-Landau equations with dynamic boundary conditions ⋮ Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates ⋮ Inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity on the upper half-plane ⋮ Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space ⋮ An initial-boundary-value problem of 2D nonlinear Schrödinger equation in a strip ⋮ INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRÖDINGER EQUATIONS

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