Publisher Summary The study of the asymptotic behavior of dynamical systems arising from
mechanics and physics is a capital issue because it is essential for practical applications to …

The main goal of this book is to present background material and recently developed
mathematical methods in the study of infinite-dimensional evolutionary models, taking into …

We study well-posedness and long-time dynamics of a class of quasilinear wave equations
with a strong damping. We accept the Kirchhoff hypotheses and assume that the stiffness …

This paper deals with the initial boundary value problem for strongly damped semilinear
wave equations with logarithmic nonlinearity utt− Δ u− Δ ut= φ p (u) log| u| in a bounded …

We present a new method of investigating the so-called quasi-linear strongly-damped wave
equations in bounded 3D domains. This method allows us to establish the existence and …

This paper is dedicated to analyzing the dynamical behavior of strongly damped wave
equations with critical nonlinearity in locally uniform spaces. After proving the global well …

A plate equation with critical exponent in locally uniform spaces with a coefficient β (x)
belonging to the locally uniform spaces Llup (RN) is studied. This equation is shown to …

We study long-time dynamics of a class of abstract second order in time evolution equations
in a Hilbert space with the damping term depending both on displacement and velocity. This …

For η\geqslant 0, we consider a family of damped wave equations u_ tt+ η Λ^ 1 2 u_t+ a u_t+
Λ u= f (u),\quad t> 0,\quad x ∈ Ω ⊂ R^ N, where− Λ denotes the Laplacian with zero …

In this paper, we consider the initial boundary problem for the Kirchhoff type wave equation.
We prove that the Kirchhoff wave model is globally well-posed in the sufficiently regular …