For a process U (t, τ): Xτ→ Xt acting on a one-parameter family of normed spaces, we
present a notion of time-dependent attractor based only on the minimality with respect to the …

This note deals with the strongly damped nonlinear wave equation with Dirichlet boundary
conditions, where both the nonlinearities f and g exhibit a critical growth, while h is a time …

We continue the analysis on the model equation arising in the theory of viscoelasticity
$$\partial_ {tt} u (t)-\big [1+ k_t (0)\big]\Delta u (t)-\int_0^\infty k'_t (s)\Delta u (ts)\ds+ f (u (t)) …

The paper is concerned with the exponential attractors for the viscoelastic wave model in
Ω⊂ R 3: u tt-ht (0) Δ u-∫ 0∞∂ sht (s) Δ u (ts) ds+ f (u)= g, with time-dependent memory …

In this paper, we consider the problem of finding the function, from the final data and where
is a linear, unbounded, self-adjoint and positive definite operator. This problem is known as …

The paper investigates the well-posedness and the complete regularity of the weak
solutions, and the existence of strong global attractor for the strongly damped wave equation …

The paper investigates longtime dynamics of the Kirchhoff wave equation with strong
dam** and critical nonlinearities: utt−(1+ ϵ‖∇ u‖ 2) Δ u− Δ u t+ h (ut)+ g (u)= f (x), with …

The paper investigates the well-posedness and the regularity of the solutions, the existence
and the continuity of the strong attractors for the structurally damped Kirchhoff wave models …

In this paper, we study the initial boundary value problem for two-dimensional strongly
damped wave equation with exponentially growing source and dam** terms. We first …

We establish the well-posedness of a strongly damped semilinear wave equation equipped
with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the …