EL PROBLEMA DE CAUCHY ASOCIADO CON UNA ECUACIÓN NO LINEAL GENERALIZADA DE SCHRÖDINGER

Omar Duque; Guillermo Rodríguez-Blanco

doi:10.18257/raccefyn.30(116).2006.2263

Vol. 30 No. 116 (2006), Mathematics

Vol. 30 No. 116 (2006)

CAUCHY'S PROBLEM ASSOCIATED WITH A NON-LINEAR GENERALIZED SCHRÖDINGER EQUATION

Mathematics

https://doi.org/10.18257/raccefyn.30(116).2006.2263

Published 2023-11-25

Omar Duque⁺⁻
Guillermo Rodríguez-Blanco⁺⁻

Omar Duque

Universidad Nacional de Colombia, Bogotá, Colombia.

Guillermo Rodríguez-Blanco

Universidad Nacional de Colombia, Bogotá, Colombia.

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How to Cite

Duque, O., & Rodríguez-Blanco, G. (2023). CAUCHY’S PROBLEM ASSOCIATED WITH A NON-LINEAR GENERALIZED SCHRÖDINGER EQUATION. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 30(116), 353–360. https://doi.org/10.18257/raccefyn.30(116).2006.2263

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Abstract

In this paper, we establish the local well-posedness for the nonlinear generalized Schrödinger equation in the Sobolev spaces H^s(R), with s > 1/2. Also, we obtain global well-posedness in H^s(R) for s = 1, 2. In addition, a blow-up result is established if the initial data belongs to F₁ (R) = H¹ (R) ∩ L²₁ (R).

https://doi.org/10.18257/raccefyn.30(116).2006.2263

Keywords

Non linear generalized Schrödinger | equation | initial value problems | local and global wellposedness | Sobolev spaces.

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