Related papers: Decay estimates for fractional wave equations on H…
We study the wave equation with potential $u_{tt}-\Delta u+Vu=0$ in two spatial dimensions, with $V$ a real-valued, decaying potential. With $H=-\Delta+V$, we study a variety of mapping estimates of the solution operators, $\cos(t\sqrt{H})$…
We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the…
In this paper, we derive several differential Harnack estimates (also known as Li-Yau-Hamilton-type estimates) for positive solutions of Fisher's equation. We use the estimates to obtain lower bounds on the speed of traveling wave solutions…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
In this paper, we investigate the spectral analysis (from the point of view of semi-groups) of discrete, fractional and classical Fokker-Planck equations. Discrete and fractional Fokker-Planck equations converge in some sense to the…
In this paper, we first establish decay estimates for the fractional and higher-order fractional H\'enon-Lane-Emden systems by using a nonlocal average and integral estimates, which deduce a result of non-existence. Next, we apply the…
This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Gr\"onwall's inequality and its discrete version are proposed. By the two inequalities, error estimates in three…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
We study the homogeneous wave equation with radially symmetric data in four or higher space dimensions. Using some new integral representations for the Riemann operator, we establish weighted decay estimates for the solution.
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…
Phenomenological expressions are derived for rates of the $\Delta (1232)$ radiative and Dalitz decays, $\Delta (1232)$ $\to N\gamma$ and $\Delta (1232)$ $\to Ne^{+}e^{-}$. Earlier calculations of these decays are commented.
We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates…
$\Omega_b \rightarrow \Omega_c^{(*)}$ semi-leptonic decays are studied in details. Relevant helicity amplitudes are written down. Both unpolarized and polarized $\Omega_b$ cases are considered. Decay angular distributions, asymmetry…