Results 101 to 110 of about 473,820 (257)
Fractional Laplacian with Supercritical Killings
Communications in Mathematical PhysicsIn this paper, we study Feynman-Kac semigroups of symmetric $\alpha$-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form $b|x|^{-\beta}$, where $b>0$ and $\beta>\alpha$. We obtain two-sided estimates on the densities $p(t, x, y)$ of these semigroups for all $t>0$, along with ...
Soobin Cho, Renming Song
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Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians
, 2020 In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal ...
Wang, Pengyan, Chen, Wenxiong
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The fractional Laplacian has infinite dimension [PDF]
Communications in Partial Differential Equations, 2019 We show that the fractional Laplacian on $\mathbb{R}^d$ fails to satisfy the Bakry- mery curvature-dimension inequality $CD( ,N)$ for all curvature bounds $ \in \mathbb{R}$ and all finite dimensions $N>0$.
Adrian Spener +2 more
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Sequences of weak solutions for fractional equations [PDF]
, 2013 This work is devoted to study the existence of infinitely many weak solutions to nonlocal equations involving a general integrodifferential operator of fractional type.
Bisci, Giovanni Molica
core
Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, EarlyView.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley +1 more source
Nonlinear Resonance Modulation in Single‐Crystalline VO2‐Integrated Si Ring Resonator
Laser &Photonics Reviews, EarlyView.This work first demonstrates a single‐crystalline VO2–Si hybrid ring resonator. The epitaxial lift‐off process enables high‐quality VO2 integration on the dissimilar Si photonic platform. The high‐quality VO2 film exhibits exceptional nonlinear resonance modulation and a steep optical transition across the metal‐insulator transition. ABSTRACT The metal‐
Sebae Park +5 more
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
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Getting Acquainted with the Fractional Laplacian [PDF]
, 2019 updated version, 72 pages, 12 ...
Abatangelo N., Valdinoci E.
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Global regularity of 2D MHD equations with almost Laplacian velocity dissipation
Boundary Value Problems, 2023 We obtain the global existence and global regularity for the 2D MHD equations with almost Laplacian velocity dissipation, which require the dissipative operators weaker than any power of the fractional Laplacian.
Linrui Li, Mingli Hong
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Numerical Investigation of a Diffusive SIR Model: Focus on Positivity Preservation
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper, we consider a system of semilinear partial differential equations (PDEs) representing a spatially extended SIR epidemic model. A brief analytical investigation of the well‐posedness and positivity of the solutions is provided in the appendix, while the main focus is on the numerical treatment of the model.
Rahele Mosleh +2 more
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