Related papers: On the effectiveness of Gamow's method for calcula…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)^{-b} with exponent depending on the…
In this paper, we study the precise decay rate in time to solutions of the Cauchy problem for the one-dimensional conservation law with a nonlinearly degenerate viscosity where the far field states are prescribed. Especially, we deal with…
In this paper, we improve the calculation of the relic gravitational waves (RGW) in two aspects: First, we investigate the transfer function after considering the redshift-suppression effect, the accelerating expansion effect, the damping…
Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these…
In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able…
This article serves as an introduction to the linear aspects of the recent submission by Krieger, Miao, and the author, see arXiv:2009.08843. It also surveys some of the results obtained on the decay of linear waves on various backgrounds…
In the present paper we show that the Temporal Wave Function approach of the decay process, which is a multicomponent version of the Time Operator approach leads to new, non-standard, predictions concerning the statistical properties of…
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 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…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…
This work first gives the global existence and optimal decay rates of solutions to the classical Timoshenko system on the framework of Besov spaces. Due to the \textit{non-symmetric} dissipation, the general theory for dissipative…
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…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
After GGH model was proposed by M. Ghisi, M. Gobbino and A. Haraux (2016), R. Ikehata and S. Iyota (2018) showed decay estimates for the total energy of solutions to GGH equations uniformly in the initial data. However, their results imply…
In this paper, we consider the long time behavior for the solution of a class of variable coefficient wave equation with nonlinear damping and logarithmic source. The existence and uniqueness of local weak solution can be obtained by using…
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…
We show in this article how perturbative approaches~from our work with Hitrik (see also the work by Anantharaman-Macia) and the {\em black box} strategy from~ our work with Zworski allow to obtain decay rates for Kelvin-Voigt damped wave…
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…
We prove a dispersive estimate for the solutions of the linearized Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a decay with respect to time t of order 1/3 for solutions with initial data in weighted Sobolev…