Document Type
Article
Publication Date
1995
Digital Object Identifier (DOI)
https://doi.org/10.1155/S0161171295000019
Abstract
For nonlinear parabolic evolution equations, it is proved that, under the assumptions of local Lipschitz continuity of nonlinearity and the dissipativity of semiflows, there exist approximate inertial manifolds (AIM) in the energy space and that the approximate inertial manifolds are constructed as the graph of the steady-state determining mapping based on the spectral decomposition. It is also shown that the thickness of the exponentially attracting neighborhood of the AIM converges to zero at a fractional power rate as the dimension of the AIM increases. Applications of the obtained results to Burgers' equation, higher dimensional reaction-diffusion equations, 2D Ginzburg-Landau equations, and axially symmetric Kuramoto-Sivashinsky equations in annular domains are included.
Rights Information
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
International Journal of Mathematics and Mathematical Sciences, v. 18, art. 928614
Scholar Commons Citation
You, Yuncheng, "Approximate Inertial Manifolds for Nonlinear Parabolic Equations Via Steady-state Determining Mapping" (1995). Mathematics and Statistics Faculty Publications. 44.
https://digitalcommons.usf.edu/mth_facpub/44
