Browsing Linear and NonLinear Waves by Issue Date
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Spectral asymptotics for $\delta$interactions on sharp cones
(2017)We investigate the spectrum of threedimensional Schr\"odinger operators with $\delta$interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ... 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(2017)We discuss here the use of nonlocal 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 ... 
Singularity formation for the 1D cubic NLS and the Schrödinger map on $\mathbb{S}^2$
(20170202)In this note we consider the 1D cubic Schrödinger equation with data given as small perturbations of a Dirac$\delta$ function and some other related equations. We first recall that although the problem for this type of ... 
Uniqueness properties for discrete equations and Carleman estimates
(20170325)Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ... 
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
(20170428)In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heatsemigroup formalism. Specifically, we combine suitable ... 
Gaussian Decay of Harmonic Oscillators and related models
(20170515)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... 
Some remarks on the $L^p$ regularity of second derivatives of solutions to nondivergence elliptic equations and the Dini condition
(20170530)In this note we prove an endpoint regularity result on the $L^P$ integrability of the second derivatives of solutions to nondivergence form uniformly elliptic equations whose second derivatives are a priori only known ... 
HartreeFock theory with a selfgenerated magnetic field
(20170601)We prove the existence of a ground state within the HartreeFock theory for atoms and molecules, in the presence of selfgenerated magnetic fields, with and without direct spin coupling. The ground state exists provided ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ... 
Sharp bounds for the ratio of modified Bessel functions
(20170621)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) ... 
El efecto de Talbot: de la óptica a la ecuación de Schrödinger
(201707)El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ... 
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(20170718)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) ... 
An efficient multigrid strategy for largescale molecular mechanics optimization
(20170801)Static mechanical properties of materials require largescale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ... 
The relativistic spherical $\delta$shell interaction in $\mathbb{R}^3$: spectrum and approximation
(20170803)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 ... 
Threedimensional coarsening dynamics of a conserved, nematic liquid crystalisotropic fluid mixture
(201709)We present a numerical investigation of the threedimensional coarsening dynamics of a nematic liquid crystalisotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ... 
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(201710)We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m1}\nabla (\Delta)^{s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ... 
Asymptotic behaviour for fractional diffusionconvection equations
(201710)We consider a convectiondiffusion model with linear fractional diffusion in the subcritical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ... 
Absence of eigenvalues of twodimensional magnetic Schr ̈odinger operators
(20171017)By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding twodimensional Schr ̈odinger operator possesses no point ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(201711)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 rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Singular Perturbation of the Dirac Hamiltonian
(20171215)This thesis is devoted to the study of the Dirac Hamiltonian perturbed by deltatype potentials and Coulombtype potentials. We analysed the deltashell interaction on bounded and smooth domains and its approximation by ...