Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity

167 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Asymptotic stability of semigroups associated with linear weak dissipative systems with memory (2007, methodology): “This can be proved by the same techniques as in [11].”
Attractors for wave equations with degenerate memory (2016, methodology): “In this case, with respect to the long-time dynamics, under the basic assumption that the function g decays exponentially, it was proved by Giorgi, Muñoz Rivera and Pata [24] that the sole dissipation given by the memory term guarantees the existence of a global attractor to the corresponding dynami”
Exponential stability in linear viscoelasticity (2006, methodology): “Then, paralleling some ideas of [11], we introduce the functionals (the first depending on the choice of s∗) Φ1(t) = − 1 κ ∫ ∞”
Stability and exponential stability in linear viscoelasticity (2009, background): “for almost every s> 0. In fact, (5.2) is quite popular in the literature, whenever one is to prove the exponential decay of solutions (see, e.g., [5, 6, 7, 8, 9, 12 , 15, 16, 17]).”
Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory (2003, unknown): “In [4], Giorgi et al.”
A New Approach to Equations with Memory (2009, background): “, in connection with the present equation, [21, 28, 42, 43]).”