Continuous families of exponential attractors for singularly perturbed equations with memory
Gatti, S, Miranville, A, Pata, V and Zelik, S (2010) Continuous families of exponential attractors for singularly perturbed equations with memory P ROY SOC EDINB A, 140. pp. 329366.
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Abstract
For a family of semigroups Sepsilon(t): Hepsilon > Hepsilon depending on a perturbation parameter epsilon is an element of [0,1], where the perturbation is allowed to become singular at epsilon = 0, we establish a general theorem on the existence of exponential attractors epsilon(epsilon) satisfying a suitable Holder continuity property with respect to the symmetric Hausdorff distance at every epsilon is an element of [0,1]. The result is applied to the abstract evolution equations with memorypartial derivative(t)x(t) + integral(infinity)(0) k(epsilon)(s)B0(x(t  s))ds + B1(x(t)) = 0, epsilon is an element of (0, 1],where k(epsilon)(s) = (1/epsilon)k(s/epsilon) is the resulting of a convex summable kernel k with unit mass. Such a family can be viewed as a memory perturbation of the equationpartial derivative(t)x(t) + B0(x(t)) + B1(x(t)) = 0,formally obtained in the singular limit epsilon > 0.
Item Type:  Article 

Divisions :  Faculty of Engineering and Physical Sciences > Mathematics 
Authors :  Gatti, S, Miranville, A, Pata, V and Zelik, S 
Date :  February 2010 
DOI :  10.1017/S0308210509000365 
Uncontrolled Keywords :  NONAUTONOMOUS DYNAMICALSYSTEMS, DAMPED WAVEEQUATION, VISCOELASTICITY, CONSTRUCTION, RELAXATION, STABILITY, LIMIT 
Depositing User :  Symplectic Elements 
Date Deposited :  28 Mar 2017 10:51 
Last Modified :  10 Jun 2019 14:00 
URI:  http://epubs.surrey.ac.uk/id/eprint/806859 
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