- 98-454 Lin G., Gao H., Duan J., Ervin V.
- Asymptotic Dynamical Difference between the Nonlocal and Local
Jun 18, 98
(auto. generated ps),
of related papers
Abstract. In this paper the difference in the asymptotic dynamics between
the nonlocal and local two-dimensional Swift-Hohenberg models
is investigated. It is shown that the bounds for the dimensions
of the global attractors for the nonlocal
and local Swift-Hohenberg models differ by an absolute constant,
which depends only on the Rayleigh number,
and upper and lower bounds of the kernel of the nonlocal
nonlinearity. Even when this kernel of the nonlocal operator
is a constant function, the dimension bounds of the global attractors
still differ by an absolute constant depending on the Rayleigh number.