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Dynamically equivalent perturbations of linear parabolic equations

Czaja R.

Demonstratio Mathematica

2004

Vol. 37, nr 2

327--348

A family of abstract parabolic equations with sectorial operator is studied in this paper. The conditions are provided to show that the global attractors for each equation exist and coincide. Although the common dynamics is simple, the examples presented in the final part of the paper indicate that the considered family may contain a linear equation together with a large number of its nonlinear perturbations. The mentioned examples include both scalar second order equations and the celebrated Cahn-Hilliard system.