Browsing Linear and Non-Linear Waves by Title
Now showing items 36-55 of 120
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Gaussian Decay of Harmonic Oscillators and related models
(2017-05-15)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... -
A geometric and physical study of Riemann's non-differentiable function
(2020-07-08)Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ... -
Geometric differentiability of Riemann's non-differentiable function
(2020-06)Riemann’s non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also ... -
Hardy uncertainty principle, convexity and parabolic evolutions
(2016-09-01)We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of ... -
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
(2019-07-02)We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
(2019-06)We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
(2020-01-01)We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ... -
Hartree-Fock theory with a self-generated magnetic field
(2017-06-01)We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ... -
Hypocoercivity of linear kinetic equations via Harris's Theorem
(2019-02-27)We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole ... -
Invariant measures for the dnls equation
(2020-10-02)We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ... -
Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$
(2017-11)Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ... -
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
(2023-10-06)In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study ... -
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(2017-06-20)We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ... -
Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
(2017)We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ... -
Magnetic domain-twin boundary interactions in Ni-Mn-Ga
(2020-04)The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ... -
Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions
(2015-12-31)In this paper, we present a mean-field model of the spin-magnetization coupling in ferromagnetic materials. The model includes non-isotropic diffusion for spin dynamics, which is crucial in capturing strong spin-magnetization ... -
Modeling cardiac structural heterogeneity via space-fractional differential equations
(2017)We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ... -
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(2017-07-18)Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... -
Numerical approximation of the fractional Laplacian on R using orthogonal families
(2020-12-01)In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the F12 Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the complex Higgins functions, the complex ... -
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
(2016-06-30)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ...