Results 31 to 40 of about 393,013 (283)
Monotone iterative technique for time-space fractional diffusion equations involving delay
Nonlinear Analysis, 2021 This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of ...
Qiang Li, Guotao Wang, Mei Wei
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Local energy estimates for the fractional Laplacian [PDF]
SIAM Journal on Numerical Analysis, 2020 The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity.
Juan Pablo Borthagaray +2 more
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A Hopf lemma for the regional fractional Laplacian [PDF]
Annali di Matematica Pura ed Applicata, 2021 We provide a Hopf boundary lemma for the regional fractional Laplacian $$(-\Delta )^s_{\Omega }$$ ( - Δ ) Ω s , with $$\Omega \subset \mathbb {R}^N$$ Ω ⊂ R N a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation $$
Nicola Abatangelo +2 more
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A Generalized Fractional Laplacian
, 2023 In this article we show that the fractional Laplacian in $R^{2}$ can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. Using this factored form we introduce a generalization of the fractional Laplacian, involving a matrix $K(x)$, suitable when the fractional Laplacian is applied in a non ...
Zheng, Xiangcheng +2 more
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Fractional Revival of Threshold Graphs Under Laplacian Dynamics
Discussiones Mathematicae Graph Theory, 2020 We consider Laplacian fractional revival between two vertices of a graph X. Assume that it occurs at time τ between vertices 1 and 2. We prove that for the spectral decomposition L=∑r=0qθrErL = \sum\nolimits_{r = 0}^q {{\theta _r}{E_r}} of the Laplacian
Kirkland Steve, Zhang Xiaohong
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Fractal and Fractional, 2022 This paper designs a new finite difference compact reconstruction unequal-sized weighted essentially nonoscillatory scheme (CRUS-WENO) for solving fractional differential equations containing the fractional Laplacian operator.
Yan Zhang, Jun Zhu
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Small Order Asymptotics of the Dirichlet Eigenvalue Problem for the Fractional Laplacian [PDF]
Journal of Fourier Analysis and Applications, 2020 We study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian (-Δ)s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Pierre Aime Feulefack +2 more
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The Pohozaev Identity for the Fractional Laplacian [PDF]
Archive for Rational Mechanics and Analysis, 2014 In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem $(- )^s u = f(u)$ in $ $, $u \equiv 0$ in $\mathbb R^n\setminus $. Here, $s\in(0,1)$, $(- )^s$ is the fractional Laplacian in $\mathbb R^n$, and $ $ is a bounded $C^{1,1}$ domain. To establish the identity we use, among other things, that if $u$ is a bounded solution
Ros Oton, Xavier +1 more
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MOND-like fractional Laplacian theory
Physical Review D, 2020 I provide a derivation of some characteristic effects of Milgrom's modified Newtonian dynamics (MOND) from a fractional version of Newton's theory based on the fractional Poisson equation.
A. Giusti
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Communications in Partial Differential Equations, 2014 14 pages; this version is considerably ...
MUSINA, Roberta, Nazarov A. I.
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