Browsing Analysis of Partial Differential Equations (APDE) by Title
Now showing items 1-20 of 266
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A Mean-field model for spin dynamics in multilayered ferromagnetic media
Chen, J.; García-Cervera, C.J.
; Yang, X. (2015-12-31)
In this paper, we develop a mean-field 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
Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2019)
Quantitative $A_1-A_\infty$ 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
Pérez, C.; Rivera-Ríos, I.P.; Roncal, L. (2016-07-01)
Quantitative $A_1-A_\infty$ 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 two-dimensional magnetic Schr ̈odinger operators
Fanelli, L.; Krejcirik, D.; Vega, L. (2017-10-17)
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 ... -
Absence of eigenvalues of two-dimensional magnetic Schroedinger operators
Fanelli, L.; Krejcirik, D.; Vega, L. (2018-01-01)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ... -
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
Lucà, R. (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), 596-647” regarding the pointwise convergence of ... -
An atomistic/continuum coupling method using enriched bases
Chen, J.; García-Cervera, C.J.; Li, X. (2015-12-31)
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 Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
Arrizabalaga, N.; Mas, A.; Vega, L. (2016-06-01)
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 infinito-dimensional
(2019-10-24)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
Alikakos, N.; Geng, Z.; Zarnescu, A. (2022-09-15)
We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ near $u=a_i$, $0<\alpha<2$. ... -
Asymptotic behaviour for fractional diffusion-convection equations
(2017-10)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 ... -
Asymptotic behaviour of neuron population models structured by elapsed-time
(2019-01-04)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
(2019-09)We study the long-time 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 self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2020-05-01)
We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although ... -
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation
Correia, S.; Côte, R.; Vega, L. (2018-07-06)
We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de 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
Kosz, D. (2022-05-27)
We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ... -
Bayesian approach to inverse scattering with topological priors
Carpio, A.; Iakunin, S.; Stadler, G. (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 Calderón--Zygmund theory on product spaces
(2019-10)We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...