Related papers: Integrated Local Energy Decay for Waves with Time-…
We study the linear wave equation on a class of spatially homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes in the decelerated regime with spatial topology $\mathbb{R}^3$. Employing twisted $t$-weighted…
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of…
We consider the Cauchy problem for wave equations with localized damping in ${\bf R}^{2}$. The damping is effective only near spatial infinity. We obtain fast energy decay estimate such that $O(t^{-2}\log t)$ as $t \to \infty$. Unlike the…
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…
We consider the damped wave equation on a compact manifold. We propose different ways of measuring decay of the energy (time averages of lower energy levels, decay for frequency localized data...) and exhibit links with resolvent estimates…
In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if replacing the damping term with a…
This paper addresses the two-dimensional initial value problem in ${\bf R}^{2}$ for the wave equation with varying spatial coefficients in the main part. Assuming compactness in the support of the initial value, we report that the…
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is called the geometric control condition. In this paper, it is…
We study the rate of decay of the energy functional of solutions of the wave equation with localized damping and a external force. We prove that the decay rates of the energy functional is determined from a forced differential equation.
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
We prove a logarithmic local energy decay rate for the wave equation with a wavespeed that is a compactly supported Lipschitz perturbation of unity. The key is to establish suitable resolvent estimates at high and low energy for the…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the…
We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory component that is integrable but not absolutely integrable. We…
In this paper we consider energy decay estimates for the Cauchy problems of dissipative wave equations with time dependent coefficients, in particular, the coefficients consisting of weak dissipation and very fast oscillating terms. For…
In this paper we consider the local energy decay result for wave equations with a short-range potential. It is important to note that one never uses a finite speed of propagation property unlike the historical previous papers. The essential…
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…
In this paper we analyze the long time behavior of a wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-differential calculus, we obtain a Carleman estimate, and then establish an estimate on…