Abstract
We consider a general scalar one-dimensional semilinear parabolic partial differential equation generating a semiflow with an attractor in an adequate state space. Generalizing known results, it is shown that this attractor is the graph of a function over a compact subset of a finite-dimensional subspace of the state space. In addition, we construct an example with a special interest for the geometric or bifurcation theory of this type of parabolic equations.
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Rocha, C. Properties of the attractor of a scalar parabolic PDE. J Dyn Diff Equat 3, 575–591 (1991). https://doi.org/10.1007/BF01049100
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DOI: https://doi.org/10.1007/BF01049100