论文信息 - On the number of determining nodes for the Ginzburg-Landau equation

On the number of determining nodes for the Ginzburg-Landau equation

In the case of the complex Ginzburg-Landau equation in one space dimension it is proven that solutions are completely determined by their values at two sufficiently close points. As a consequence, an upper bound for the winding number of stationary solutions is established in terms of the bifurcation parameters. It is also proven that the fractal dimension of the set of stationary solutions is less than or equal to 4.

Igor Kukavica | I. Kukavica

[1] F. Takens. Detecting strange attractors in turbulence , 1981 .

[2] Jean-Michel Ghidaglia,et al. Dimension of the attractors associated to the Ginzburg-Landau partial differential equation , 1987 .

[3] Darryl D. Holm,et al. Low-dimensional behaviour in the complex Ginzburg-Landau equation , 1988 .

[4] Keith Promislow,et al. Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equations , 1991 .

[5] R. Temam,et al. Gevrey class regularity for the solutions of the Navier-Stokes equations , 1989 .

[6] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[7] R. Temam,et al. Determination of the solutions of the Navier-Stokes equations by a set of nodal values , 1984 .

[8] Charles R. Doering,et al. On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation , 1990 .