Attractors for reaction-diffusion equations: existence and estimate of their dimension
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 25 (1-2) , 101-147
- https://doi.org/10.1080/00036818708839678
Abstract
In this paper, we study some questions related to attractors for two types of reaction-diffusion equations : an equation with a polynomial growth nonlinearity and systems admitting a positively invariant region. For these problems, we prove the existence of a maximal attractor which describes the long-time behaviour of the solutions and we derive estimates of its Hausdorff and fractal dimensions in terms of the data. Our results are applied to several classical equations.Keywords
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