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Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems
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Robinson, James C., Rodriguez-Bernal, Anibal and Vidal-Lopez, Alejandro (2007) Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Journal of Differential Equations, Vol.238 (No.2). pp. 289-337. doi:10.1016/j.jde.2007.03.028 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2007.03.028
Abstract
We analyse the dynamics of the non-autonomous nonlinear reaction-diffusion equation u(t) - Delta u = f(t, x, u),
subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our main assumption is that the nonlinear term satisfies a bound of the form f(t, x, u)u <= C(t, x)vertical bar u vertical bar(2) + D(t, x)vertical bar u vertical bar, where the linear evolution operator associated with Delta + C(t, x) is exponentially stable. As an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non-autonomous linear problem u(t) - Delta u = C(t, x)u between different L-P spaces. (c) 2007 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 15 July 2007 | ||||
Dates: |
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Volume: | Vol.238 | ||||
Number: | No.2 | ||||
Number of Pages: | 49 | ||||
Page Range: | pp. 289-337 | ||||
DOI: | 10.1016/j.jde.2007.03.028 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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