Browsing Linear and Non-Linear Waves by Title
Now showing items 72-91 of 120
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Pointwise Convergence of the Schr\"odinger Flow
(2021-01)In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain ... -
A pseudospectral method for the one-dimensional fractional Laplacian on R
(2021-01-15)In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ... -
Pseudospectral Methods for the Fractional Laplacian on R
(2020-07-02)In this thesis, first, we propose a novel pseudospectral method to approximate accu- rately and efficiently the fractional Laplacian without using truncation. More pre- cisely, given a bounded regular function defined over ... -
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
(2022-01-01)The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 ... -
Reconstruction from boundary measurements for less regular conductivities
(2016-10-01)In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz ... -
Regularity of fractional maximal functions through Fourier multipliers
(2018)We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ... -
Relativistic Hardy Inequalities in Magnetic Fields
(2014-12-31)We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality ... -
The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
(2017-08-03)This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... -
Riemann's non-differentiable function and the binormal curvature flow
(2020-07-14)We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
(2019)Abstract. We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations ∂tu − Lσ,μ[φ(u)] = f(x,t) in RN × (0,T), where Lσ,μ is a general ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
(2018)\noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ... -
The Schrödinger equation and Uncertainty Principles
(2020-09)The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution. First we consider the elliptic Schrödinger ... -
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
(2018)We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ... -
Self-adjointness of two-dimensional Dirac operators on corner domains
(2021-01-01)We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... -
Self-similar dynamics for the modified Korteweg-de Vries equation
(2019-04-09)We prove a local well posedness result for the modified Korteweg-de Vries equa- tion in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around ... -
Sensitivity of twin boundary movement to sample orientation and magnetic field direction in Ni-Mn-Ga
(2019)When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni- Mn-Ga stick, twin boundaries move instantaneously or gradullay through the sample. We evaluate the sample shape dependence ... -
Sharp bounds for the ratio of modified Bessel functions
(2017-06-21)Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with $W_{\nu }\left( x\right) ... -
Sharp exponential localization for eigenfunctions of the Dirac Operator
(2018)We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ... -
Sharp local smoothing estimates for Fourier integral operators
(2019)The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ... -
A sharp lorentz-invariant strichartz norm expansion for the cubic wave equation in \mathbb{R}^{1+3}
(2020)We provide an asymptotic formula for the maximal Stri- chartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz ...