Related papers: Bilinear local smoothing estimate for Airy equatio…
We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…
We first review the $L^2$ bilinear generalizations of the $L^4$ estimate of Strichartz for solutions of the homogeneous 3D wave equation, and give a short proof based solely on an estimate for the volume of intersection of two thickened…
We consider refinements of the local smoothing estimates for the Schr\"odinger equation in domains which are exterior to a strictly convex obstacle in $\RR^n$. By restricting the solution to small, frequency dependent collars of the…
In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined.…
It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are also discussed.
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 an endpoint multilinear estimate for the $X^{s,b}$ spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global…
In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
The bilinear estimtate in proposition 7.15 [J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Parts II, Geometric Funct. Anal. 3(3) (1993) 209-262.] plays an essential…
By considering the features of the airport runway image filtering, an improved bilateral filtering method was proposed which can remove noise with edge preserving. Firstly the steerable filtering decomposition is used to calculate the…
We consider the problem of establishing nonlinear smoothing as a general feature of nonlinear dispersive equations, i.e. the improved regularity of the integral term in Duhamel's formula, with respect to the initial data and the…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
We discuss the microlocal Gevrey smoothing effect for the Schr\"odinger equation with variable coefficients via the propagation property of the wave front set of homogenous type. We apply the microlocal exponential estimates in a Gevrey…
This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous…
In this paper we prove bilinear Strichartz estimates for a solution to the Schr{\"o}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$. These…
For bilinear Fourier multipliers that contain some oscillatory factors, boundedness of the operators between Lebesgue spaces is given including endpoint cases. Sharpness of the result is also considered.
We study a damped semi-linear wave equation in a bounded domain with smooth boundary. It is proved that any sufficiently smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset…
We consider semilinear equations of the form p(D)u=F(u), with a locally bounded nonlinearity F(u), and a linear part p(D) given by a Fourier multiplier. The multiplier p(\xi) is the sum of positively homogeneous terms, with at least one of…
It is well known that phase function methods allow for the numerical solution of a large class of oscillatory second order linear ordinary differential equations in time independent of frequency. Unfortunately, these methods break down in…