Attractors for a damped hyperbolic equation with linear memory

By Vittorino Pata, A. Zucchi. 2001

194 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.

Singular limit of differential systems with memory (2006, background): “A similar argument applies verbatim to the damped wave equation with memory, and, in general, to partial differential equations with memory of the second order in time (see [13, 22] for the details).”
Exponential stability in linear viscoelasticity (2006, unknown): “In particular, the third component of the solution S(t)(u0, v0, η0) = (u(t), ∂tu(t), η) has the explicit representation formula (see [16]) η(s) = { u(t) − u(t − s), 0 < s ≤ t, η0(s − t) + u(t) − u0, s > t.”
Attractors for wave equations with degenerate memory (2016, methodology): “1) With respect to the variable η it is shown in Pata and Zucchi [32] that η t = v− η s, η(0)= 0, can be considered as η t = v − T η , where”