Related papers: Decay estimates for fractional wave equations on H…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
This note is devoted to exploring some analytic-geometric properties of the regularity and capacity associated to the so-called fractional dissipative operator $\partial_t+(-\Delta)^\alpha$, naturally establishing a diagonally sharp…
We study the hyperboloidal initial value problem for the one-dimensional wave equation perturbed by a smooth potential. We show that the evolution decomposes into a finite-dimensional spectral part and an infinite-dimensional radiation…
The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can be used to prove uniqueness of weak solutions to such…
In this study, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{eqnarray*} D^{\alpha}\left(u(t)\right)&=&p(t)g\left(v(\sigma(t))\right),\\…
An angular analysis and a measurement of the differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$ are presented, using data corresponding to an integrated luminosity of $3.0\, {\rm fb^{-1}}$ of $pp$ collisions recorded by…
We obtain refined Strichartz estimates for the sub-Riemannian Schr\"{o}dinger equation on $H$-type Carnot groups using Fourier restriction techniques. In particular, we extend the previously known Strichartz estimates previously obtained…
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…
We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-\Delta+V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^\alpha V(x)=O(|x|^{-\delta})$ for $|x|>1$, where…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
We prove that the operator $L_0=-(1+|x|)^\beta(-\Delta)^{\alpha/2}$ with $\alpha\in(0,2)$, $d>\alpha$ and $\beta\ge0$ generates a compact semigroup or resolvent on $L^2(\R^d;(1+|x|)^{-\beta}\,dx)$, if and only if $\beta>\alpha$. When…
We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $\dot{u}(t,x) = u''(t,x) +u(t,x)(1-u(t-h,x)),$ $x \in \mathbb{R},\ t >0;$ where $h>0.$ As a consequence, we show the exponential stability, with an…
Contributions to the decay rates of P-wave charmonium states that are proportional to $n_f \alpha_s^3$, where $n_f$ is the number of flavors of light quarks, are calculated in the framework of nonrelativistic QCD using the threshold…
The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to…
A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived for diffusion semigroups on…
This article gives an energy decay result for small data solutions to a class of semilinear wave equations in two space dimensions possessing weakly dissipative structure relevant to the Agemi condition.
Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and…
In this work, we obtain decay bounds for a class of ID dispersive equations that includes the linearized water wave. These decay bounds display a surprising growth factor, which we show is sharp, The proofs rely on careful analysis of…
We compute energy distributions of three $\alpha$-particles emerging from the decay of $^{12}$C resonances by means of the hyperspherical adiabatic expansion method combined with complex scaling. The large distance continuum properties of…