Abstract
In this paper, we prove that a Lipschitz perturbed map of a gradient Morse–Smale diffeomorphism T on Rm has the Lipschitz shadowing property on a neighborhood of the global attractor AT, and apply the result to get the structural stability and the rate of convergence of global attractors of Chafee–Infante equations under Lipschitz perturbations of the domain and equation.
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