Generalized Convergence and Uniform Bounds for Semigroups of Restrictions of Nonselfadjoint Operators

In Pellicer (Nonlinear Anal. 69:3110–3127, 2008) we showed the existence of exponentially attracting invariant manifolds for a nonlinear strongly damped viscoelastic problem. In that paper we used an special result, that we did not prove there, concerning certain uniform bounds for families of semig...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2010-09, Vol.22 (3), p.399-411
Main Author: Pellicer, Marta
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:In Pellicer (Nonlinear Anal. 69:3110–3127, 2008) we showed the existence of exponentially attracting invariant manifolds for a nonlinear strongly damped viscoelastic problem. In that paper we used an special result, that we did not prove there, concerning certain uniform bounds for families of semigroups generated by restrictions of nonselfadjoint linear operators. The fact of applying this to nonselfadjoint operators represented the main novelty and difficulty of Pellicer (2008). In the present paper we prove this special result that was used in Pellicer (2008). This is done using the notion of generalized convergence between operators.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-010-9184-z