We study the energy decay rate of Kelvin–Voigt damped wave equation with piecewise smooth damping on multi-dimensional domain. Under suitable geometric assumptions support damping, we obtain optimal polynomial which turns out to be different from one-dimensional case studied in Liu and Rao [Z. Angew. Math. Phys. 56 (2005), no. 4, 630–644]. This is saturated by high quasi-modes localized optics ...

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc, using Fourier and generalized Laguerre functions. As an example, we consider a nonlinear strongly damped wave equation. The mixed spectral and pseudospectral schemes are proposed. The convergence is proved. Numerical results demonstrate the efficiency of this approach. AMS su...

The existence and Hausdorff dimension of the global attractor for discretization of a damped wave equation with the periodic nonlinearity under the periodic boundary conditions are studied for any space dimension. The obtained Hausdorff dimension is independent of the mesh sizes and the space dimension and remains small for large damping, which conforms to the physics.

Abstract In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. particular, under some proper assumptions, prove that attractor $\{A_{\varepsilon }(t)\}_{t\in \mathbb{R}}$ { A ? <mml:m...

This paper investigates a damped stochastic wave equation driven by a non-Gaussian Lévy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition semigroup under mild conditions.

In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence of a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

In this paper, we establish the existence and describe the global structure of traveling waves for a class of lattice delay differential equations describing cellular neural networks with distributed delayed signal transmission. We describe the transition of wave profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. We a...