Abstract
For the scalar reaction diffusion equation with Dirichlet boundary conditions, it is proved that its maximal compact attractor is the graph of a C1 function from a subset with nonempty interior of a subspace of the state space the dimension of which is equal to the maximal Morse index of the equilibria of the equation.
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Brunovský, P. The attractor of the scalar reaction diffusion equation is a smooth graph. J Dyn Diff Equat 2, 293–323 (1990). https://doi.org/10.1007/BF01048948
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DOI: https://doi.org/10.1007/BF01048948