On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation

There are five chapters in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line problem for the Ginzburg-Landau equation are established: (1) local existence-uniqueness; (2) small amplitude solution; (3) criteria for global existence. In Chapter 5, the weak solution to an initial-boundary value problem for the GL equation is obtained via Galerkin's method.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Bu, Qiyue

Contributors dc:contributor

• Carroll, R.

• Applied Mechanics
• Mathematics

Identifier

(UMI)AAI9236403

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72530