Artículos de revistas
Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation.
Fecha
2014-02Registro en:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge, v.144A, n.1, p.13-51, 2014
10.1017/S0308210511001235
Autor
Carvalho, Alexandre Nolasco de
Cholewa, Jan W.
Dlotko, Tomasz
Institución
Resumen
We consider a family of bounded dissipative asymptotically compact semigroups depending on a parameter, and study the continuity properties of the corresponding family of its global attractors. We exploit the idea of the uniform exponential attraction property to discuss the continuity properties of the family of attractors and estimate the rate of convergence of the approximating attractors to the limit one. Showing a range of applications of an abstract framework, we focus much of our attention on a perturbed damped wave equation. In this latter case our results involve nonlinearities with critical exponents, for which the continuity of the Family of attractors is concluded, including the rate of convergence and the regularity of the limit attractor. This complements the results in the literature.