- 95-463 Duan, J., Ly, H. and Titi, E. S.
- The Effect of Nonlocal Interactions on the Dynamics of the
Oct 18, 95
(auto. generated ps),
of related papers
Abstract. Nonlocal amplitude equations of the complex Ginzburg-Landau
type arise in a few physical contexts, such as in ferromagnetic
systems. In this paper, we study the effect of the nonlocal term on
the global dynamics by considering a model nonlocal complex amplitude
equation. First, we discuss the global existence, uniqueness and
regularity of solutions to this equation. Then we prove the existence
of the global attractor, and of a finite dimensional inertial
manifold. We provide upper and lower bounds to their dimensions, and
compare them with those of the cubic complex Ginzburg-Landau equation.
It is observed that the nonlocal term plays a stabilizing or
destabilizing role depending on the sing of the real part of its
coefficient. Moreover, the nonlocal term affects not only the diameter
of the attractor but also its dimension.