Browsing Linear and Non-Linear Waves by Title
Now showing items 21-40 of 78
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Evolution of Polygonal Lines by the Binormal Flow
(Springer Nature Switzerland AG 2020, 2020-02-05)The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ... -
Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers
(Archive for Rational Mechanics and Analysis, 2020-07)In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results ... -
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(submitted, 2017-10)We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ... -
Gaussian Decay of Harmonic Oscillators and related models
(Journal of Mathematical Analysis and Applications, 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
(Advances in Mathematics, 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
(Communications in Mathematical Physics, 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
(Revista Matemática Complutense, 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
(Revista Matemática Complutense, 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: ... -
Hartree-Fock theory with a self-generated magnetic field
(Journal of Mathematical Physics, 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
(Kinetic & Related Models, 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 ... -
Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$
(Analysis & PDE, 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 ... -
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(Mathematische Nachrichten, 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
(Boundary Value Problems, 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 ... -
Mean-field dynamics of the spin-magnetization coupling in ferromagnetic materials: Application to current-driven domain wall motions
(IEEE Transactions on Magnetics, 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
(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 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
(Mathematical Inequalities & 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) ... -
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
(Communications in Partial Differential Equations, 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 ... -
On the energy of critical solutions of the binormal flow
(2019-07-20)The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ... -
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
(2019-09-03)In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ...