University of Illinois Urbana-Champaign

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

Bu, Qiyue

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https://hdl.handle.net/2142/72530

Description

Title
On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation
Author(s)
Bu, Qiyue
Issue Date
1992
Doctoral Committee Chair(s)
Carroll, R.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Applied Mechanics
  • Mathematics
Abstract
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.
Graduation Semester
1992
Type of Resource
text
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http://hdl.handle.net/2142/72530

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