Qualitative Property Of Solutions For The Complex Ginzburg-Landau Type Equation

The time-dependent complex Ginzurg-Landau partial differential equation has been used to simplified model phenomena in a number of different areas in physics mechanics and other areas. In this dissertation we discuss three types complex Ginzurg-Landau equations.In chapter 2, we first discuss the complex Ginzurg-Landau equationsaccording to the conditions that solutions exist, we derive a prior estimates that indicate that solutions depend continuously on some parameters in the governing differential equation μ,ν,αSecondly, in chapter 3, continuous dependence on a modelling parameter is established for solutions of a problem for a complex Ginzurg-Landau equation with p-Laplacian.In chapter 4, the complex Ginzurg-Landau type equation is considered:through the first eigenvalue λ > 0 and the corresponding first eigenfunction φ(x) > 0, we obtain a series of growth estimates of the solutions for the complex Ginzurg-Landau type equation in finite time. By means of the estimates, we investigate the blow up properties of the solutions in finite time. Furthermore, it is coincided with some results of the nonlinear Schrodinger equation when some parameters in the complex Ginzurg-Landau type equation tend to zero.