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  

Authors : 


Date :  February 2010  
Identification Number :  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 :  31 Oct 2017 17:14  
URI:  http://epubs.surrey.ac.uk/id/eprint/806859 
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