Abstract
In this paper we study topological structural stability for a family of nonlinear semigroups \(T_h(\cdot )\) on Banach space \(X_h\) depending on the parameter h. Our results shows the robustness of the internal dynamics and characterization of global attractors for projected Banach spaces, generalizing previous results for small perturbations of partial differential equations. We apply the results to an abstract semilinear equation with Dumbbell type domains and to an abstract evolution problem discretized by the finite element method.
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