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Graduate Thesis of Rodrigo Véjar

Véjar, RodrigoProgramPhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción
Enrollment Year2015
Senior Year2019
Thesis TitleStudy of Stability and Numerical Conservative Methods for the High Order Schrödinger Equation

Thesis Summary:

The present thesis contains contributions associated to three different contexts. The fi rst one proposes a fi nite difference scheme that solves a High Order Nonlinear Schrödinger equation (HNLS) in one dimension, scheme that also has conservation and stabilization properties, if a certain damping function is present. The second one deals with a Nonlinear Schrödinger equation (NLS) in two dimensions, where a fi nite volume scheme was used to approximate the solution when a localized damping function is present. The scheme replicates a stabilization result proved by Cavalcanti, Corrêa, Ozsari, Sepúlveda y Véjar-Asem. In the third contribution, a hanging bridge problem is solved numerically using a fi nite difference scheme. The scheme also manages to replicate a stabilization result proved in Domingos Cavalcanti, M. Cavalcanti, Corrêa, Hajjej, Sepúlveda, y Véjar Asem.

Thesis Director(s) Marcelo M. Cavalcanti, Mauricio Sepúlveda
Thesis Project Approval Date2017, June 02
Thesis Defense Date2019, December 16
Professional Monitoring
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ISI Publications from the Thesis

Marcelo CAVALCANTI, Wellington CORREA, Andrei V. FAMINSKII, Mauricio SEPúLVEDA, Rodrigo VéJAR: Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation. Computers & Mathematics with Applications, vol. 96, pp. 188-208, (2021).

Marcelo CAVALCANTI, Wellington CORREA, Türker ÖZSARI, Mauricio SEPúLVEDA, Rodrigo VéJAR: Exponential stability for the nonlinear Schrödinger equation with locally distributed damping. Communications in Partial Differential Equations, vol. 45, 9, pp. 1134-1167, (2020).

Marcelo CAVALCANTI, Wellington CORREA, André DOMINGOS, Zaid HAJJEJ, Mauricio SEPúLVEDA, Rodrigo VéJAR: Uniform decay rates for a suspension bridge with locally distributed nonlinear damping. Journal of the Franklin Institute, vol. 357, 4, pp. 2388-2419, (2020).

Marcelo CAVALCANTI, Wellington CORREA, Mauricio SEPúLVEDA, Rodrigo VéJAR: Finite difference scheme for a higher order nonlinear Schrödinger equation. Calcolo, vol. 56, 4, article:40, (2019).

Marcelo CAVALCANTI, Wellington CORREA, Mauricio SEPúLVEDA, Rodrigo VéJAR: Finite difference scheme for a high order nonlinear Schrödinger equation with localized damping. Studia Universitatis Babeș-Bolyai Mathematica, vol. 64, 2, pp. 161-172, (2019).

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