Lower regularity solutions of the biharmonic Schrödinger equation in a quarter plane

DOI10.2140/PJM.2020.309.35zbMath1464.35312arXiv1812.11079OpenAlexW2907965536MaRDI QIDQ2226643

Fernando A. Gallego, Roberto de A. Capistrano-Filho, Márcio André Araújo Cavalcante

Publication date: 9 February 2021

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11079

zbMATH Keywords

initial-boundary value problemlocal well-posednessbiharmonic Schr\odinger equationquarter plane.

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Boundary value problems for nonlinear higher-order PDEs (35G30) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Boundary value problems for linear higher-order PDEs (35G15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (11)

Regularity properties of the cubic biharmonic Schrödinger equation on the half line ⋮ Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line ⋮ Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation ⋮ The global solution of anisotropic fourth-order Schrödinger equation ⋮ Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane ⋮ Exact boundary controllability of the linear biharmonic Schrödinger equation with variable coefficients ⋮ Error estimates of finite difference methods for the biharmonic nonlinear Schrödinger equation ⋮ Low regularity well-posedness for dispersive equations on semi-infinite intervals ⋮ Stabilization and control for the biharmonic Schrödinger equation ⋮ Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation ⋮ Controllability for Schrödinger type system with mixed dispersion on compact star graphs

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