Browsing Analysis of Partial Differential Equations (APDE) by Title
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A Meanfield model for spin dynamics in multilayered ferromagnetic media
(20151231)In this paper, we develop a meanfield model for describing the dynamics of spintransfer torque in multilayered ferromagnetic media. Specifically, we use the techniques of Wigner transform and moment closure to connect the ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(2019)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $\BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(20160701)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
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 ... 
Absence of eigenvalues of twodimensional magnetic Schroedinger operators
(20180101)By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding twodimensional Schroedinger operator possesses no point ... 
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
(2022)We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596647” regarding the pointwise convergence of ... 
An atomistic/continuum coupling method using enriched bases
(20151231)A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to ... 
An IsoperimetricType Inequality for Electrostatic Shell Interactions for Dirac Operators
(20160601)In this article we investigate spectral properties of the coupling $H + V_{\lambda}$, where $H =i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$, $m>0$ and $V_{\lambda}$ is an electrostatic shell ... 
Análisis de Fourier en el toro infinitodimensional
(20191024)Se presentan algunos resultados originales de análisis armónico para funciones definidas en el toro infinito, que es el grupo topológico compacto consistente en el producto cartesiano de una familia numerable de toros ... 
Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(20220915)We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of AllenCahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim ua_i^\alpha$ near $u=a_i$, $0<\alpha<2$. ... 
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 ... 
Asymptotic behaviour of neuron population models structured by elapsedtime
(20190104)We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ... 
Asymptotic behaviour of some nonlocal equations in mathematical biology and kinetic theory
(201909)We study the longtime behaviour of solutions to some partial differential equations arising in modeling of several biological and physical phenomena. In this work, the type of the equations we consider is mainly nonlocal, ... 
Asymptotic models for free boundary flow in porous media
(2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ... 
Asymptotics in Fourier space of selfsimilar solutions to the modified Kortewegde Vries equation
(20180706)We give the asymptotics of the Fourier transform of selfsimilar solutions to the modified Kortewegde Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ... 
Asymptotics in Fourier space of selfsimilar solutions to the modified Kortewegde Vries equation
(20200501)We give the asymptotics of the Fourier transform of selfsimilar solutions for the modified Kortewegde Vries equation. In the defocussing case, the selfsimilar profiles are solutions to the Painlevé II equation; although ... 
Asymptotics in Fourier space of selfsimilar solutions to the modified Kortewegde Vries equation
(20180706)We give the asymptotics of the Fourier transform of selfsimilar solutions to the modified Kortewegde Vries equation, through a fixed point argument in weighted W1,8 around a carefully chosen, two term ansatz. Such knowledge ... 
A∞ condition for general bases revisited: complete classification of definitions
(20220527)We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, MartínReyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ... 
Bayesian approach to inverse scattering with topological priors
(2020)We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite ... 
Bilinear CalderónZygmund theory on product spaces
(201910)We develop a wide general theory of bilinear biparameter singular integrals $T$. This includes general Calder\'onZygmund type principles in the bilinear biparameter setting: easier bounds, like estimates in the Banach ...