On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type

Asymptotic profiles for a strongly damped plate equation with lower order perturbation

“…Under these conditions it is well-known that the problem (1)-(2) has a unique weak solution u ∈ C([0, +∞); H 2 (R n ))∩C 1 ([0, +∞); L 2 (R n )).This type of physical model is well-studied by many mathematicians (cf., Silva-Ma [16] and the references therein). The first purpose is to find precise decay estimates of the L 2 -norm of solutions u(t, x) to problem (1)- (2).…”

Global attractor for suspension bridge equations with memory

“…Later, Park and Kang generalized the results of . Jorge Silva and Ma proved the exponential stability and global attractor of plate equations with memory and perturbation of p ‐Laplacian type. Oliveira Araújo et al .…”

“…In recent years, the asymptotic behavior of evolution equations with memory effects have been studied by many authors (see, and references therein). In order to construct a dynamical system corresponding to a model with memory, they use the so‐called history space setting, which was proposed by Dafermos .…”

Long-time dynamics for a class of Kirchhoff models with memory

“…We emphasize that for Kirchhoff models in spaces with dimension N ≥ 3, the strong dissipation − u t seems to play an important role as discussed in Jorge Silva and Ma, 16 when some technical difficulties inherent in the p-Laplacian operator p u = div(|∇u| p−2 ∇u) appear. In this case, for N ≥ 3, the well-posedness of Kirchhoff models without strong damping is not known.…”