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Title: Nonlinear Schrodinger equations with variable coefficients
Keywords: Nonlinear Schrodinger equations, Variable coefficients, Non-autonomous, Inhomogeneous, Existence, Blow-up
Issue Date: 12-Nov-2003
Citation: TANG HONGYAN (2003-11-12). Nonlinear Schrodinger equations with variable coefficients. ScholarBank@NUS Repository.
Abstract: This Thesis focuses on the cubic nonlinear Schrodinger equations (NLS) with variable coefficients. First, we consider the Cauchy problem for the vector-valued NLS with space- and time-dependent coefficients on N-dimensional entire space and torus. By an approximation argument we prove that for suitable initial maps, the Cauchy problem admits unique local solutions, which preserve the regularity of the initial data. We also discuss the global existence in the cases N=1, 2. Second, we study blow-up solutions to the Cauchy problem of the inhomogeneous scalar NLS with spatial dimension two, and investigate some qualitative properties of blow-up solutions when they exist.
Appears in Collections:Ph.D Theses (Open)

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