We consider the wave equation with a delay term in dynamical control. If is small enough, we establish strong stability of this system, but show that it not exponentially stable. then prove system has same rational decay rate than one without delay.

In the continuum O(3) sigma-model description of gapped spin systems, S = 1 magnons can only decay into three lower energy magnons. We argue that the symmetry of the quantum spin Hamiltonian often allows decay into two magnons, and compute this decay rate in model systems. Two-magnon decay is present in Haldane gap S = 1 spin chains, even though it cannot be induced by any allowed term written ...

We study numerically the decay of the innaton by solving the full non-linear equations of motion on the lattice. We connrm that parametric resonance is eeective in transferring energy from the innaton to a scalar eld as long as the self-interactions of the second eld are very small. However, in the very broad resonance case (q 1) the decay rate is limited by scatterings, which signiicantly slow...

<p style='text-indent:20px;'>This paper is on the asymptotic behavior of elastic string equation with localized Kelvin-Voigt damping</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}(x, t)-[u_{x}(x, t)+b(x)u_{x, t}(x, t)]_{x} = 0, \; x\in(-1, 1), t>0, $\end{document} </tex-math></disp-formula&...

In this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t local uniform decay rate (Price’s law [54]) for linear waves. As a corollary, we also prove Pric...