This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...

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 ...

By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ...

We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...

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 ...

We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...

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 ...

Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...

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) ...

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 ...