Asymptotic behavior of a delayed wave equation without displacement term

Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time-Delayed Degenerate Diffusion Equation

and Applied Analysis 3 (a) (b) Figure 1: Sharp-type traveling wave fronts. (a) Monotonic increasing. (b) Monotonic decreasing. (a) (b) Figure 2: Smooth-type traveling wave fronts. (a) Monotonic increasing. (b) Monotonic decreasing. Clearly, for any given φ > 0, if

Asymptotic Behavior of Solutions of Time-delayed Burgers’ Equation

In this paper, we consider the Burgers’ equation with a time delay. By using the Liapunov function method, we show that the delayed Burgers’ equation is exponentially stable if the delay parameter is sufficiently small. We also give an explicit estimate of the delay parameter in term of the viscosity and the initial condition, which indicates that the delay parameter tends to zero if the initia...

Asymptotic Behavior of Solutions to the Finite-Difference Wave Equation

where up in Eq. (2) corresponds to u(jôx, not) in Eq. (1), and where a = cSt/Sx. Here öt and Sx are the time and space intervals, respectively. We consider the case — co < x < », í > 0. It was shown by Courant, Friedrichs, and Lewy in a wellknown paper [1] that if up and u,x are prescribed for ally, then the computational process represented by Eq. (2) will yield values for w/ which converge to...

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

Asymptotic Behavior of Stochastic Strongly Wave Equation on Unbounded Domains

We study the asymptotic behavior of solutions to the stochastic strongly damped wave equation with additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence of a random attractor.