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Mathematical analysis of plasmon resonances for curved nanorods 曲面纳米棒等离子体共振的数学分析
Pub Date : 2020-07-22 DOI: 10.1016/J.MATPUR.2021.07.010
Youjun Deng, Hongyu Liu, G. Zheng
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引用次数: 19
Local Well Posedness of the Euler–Korteweg Equations on $${{mathbb {T}}^d}$$ 上Euler-Korteweg方程的局部适定性 $${{mathbb {T}}^d}$$
Pub Date : 2020-07-22 DOI: 10.1007/S10884-020-09927-3
M. Berti, A. Maspero, F. Murgante
{"title":"Local Well Posedness of the Euler–Korteweg Equations on $${{mathbb {T}}^d}$$","authors":"M. Berti, A. Maspero, F. Murgante","doi":"10.1007/S10884-020-09927-3","DOIUrl":"https://doi.org/10.1007/S10884-020-09927-3","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86925164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A one-dimensional symmetry result for entire solutions to the Fisher-KPP equation Fisher-KPP方程全解的一维对称性结果
Pub Date : 2020-07-20 DOI: 10.1090/proc/15415
C. Sourdis
We consider the Fisher-KPP reaction-diffusion equation in the whole space. We prove that if a solution has, to main order and for all times (positive and negative), the same exponential decay as a planar traveling wave with speed larger than the minimal one at its leading edge, then it has to coincide with the aforementioned traveling wave.
我们考虑整个空间中的Fisher-KPP反应扩散方程。我们证明,如果一个解在主阶和所有时间(正负)具有与平面行波相同的指数衰减,且速度大于其前缘的最小速度,则它必须与上述行波重合。
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引用次数: 1
Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains 达西定律作为可压缩流体在穿孔区域的低马赫数和均匀化极限
Pub Date : 2020-07-17 DOI: 10.1142/s0218202521500391
Karina Kowalczyk, Richard Hofer, S. Schwarzacher
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is increasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy's law. The range of sizes of particles we consider are exactly the same which lead to Darcy's law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovskiu{i} operator This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents $gamma> frac32$.
本文研究了由周期分布的相同粒子穿孔的三维区域中可压缩正压Navier-Stokes方程的均匀化极限。我们研究了粒子大小和距离的变化规律,使得粒子的体积分数趋于零,而它们的阻力密度趋于无穷大。假设马赫数以一定的速率增加,微观系统的速度和压力的重新标度收敛于一个有效方程的解,该方程由达西定律给出。我们考虑的颗粒大小范围完全相同,这导致了不可压缩流体均质极限中的达西定律。与Darcy状态的先前结果不同,我们通过Bogovski u{i}算子估计与压力近似相关的亏值,这允许更灵活地估计Lebesgue和Sobolev空间中的压力,并允许证明所有正压指数的收敛结果$gamma> frac32$。
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引用次数: 12
Existence and improved regularity for a nonlinear system with collapsing ellipticity 具有塌缩椭圆的非线性系统的存在性及改进正则性
Pub Date : 2020-07-16 DOI: 10.2422/2036-2145.201903_006
Edgard A. Pimentel, J. M. Urbano
We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an improved $mathcal{C}^{1,text{log-Lip}}$-regularity estimate using tangential analysis methods. The system illustrates a sophisticated version of the proverbial thermistor problem and our results are new even in simpler modelling scenarios.
研究了一个由混合奇异/简并型椭圆方程和低可积源泊松方程组成的非线性系统。我们证明了一个弱解在任意空间维度上的存在性,并主要利用切向分析方法导出了一个改进的$mathcal{C}^{1,text{log-Lip}}$-正则性估计。该系统说明了众所周知的热敏电阻问题的复杂版本,即使在更简单的建模场景中,我们的结果也是新的。
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引用次数: 0
A triviality result for semilinear parabolic equations 半线性抛物方程的一个平凡结果
Pub Date : 2020-07-15 DOI: 10.3934/MINE.2022002
G. Catino, D. Castorina, C. Mantegazza
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation begin{equation*} u_{t}=Delta u + |u|^{p} end{equation*} on complete Riemannian manifolds of dimension $n geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $frac{n+2}{n-2}$.
当$p$小于临界Sobolev指数$frac{n+2}{n-2}$时,我们给出了半线性热方程begin{equation*} u_{t}=Delta u + |u|^{p} end{equation*}在具有非负Ricci张量的$n geq 5$维完全黎曼流形上的“点向”单调时间上的有界“永恒”解的平凡性结果。
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引用次数: 3
Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured euclidean space 刺穿欧几里得空间中快速扩散方程奇异解的渐近行为
Pub Date : 2020-07-14 DOI: 10.3934/DCDS.2021085
K. M. Hui, Jinwan Park
We study the existence, uniqueness, and asymptotic behaviour of the singular solution of the fast diffusion equation, which blows up at the origin for all time. For $nge 3$, $0
研究了在原点时刻爆炸的快速扩散方程奇异解的存在性、唯一性和渐近性。对于$nge 3$, $0
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引用次数: 1
Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow 不可压缩流体流动耦合的具有群集项的Vlasov方程的时间衰减和渐近行为
Pub Date : 2020-07-13 DOI: 10.1016/J.NONRWA.2021.103410
Young-Pil Choi, K. Kang, Hwa Kil Kim, Jae‐Myoung Kim
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引用次数: 1
Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces 具有对准力和非局部力的vlasov型方程的水动力极限的定量化
Pub Date : 2020-07-09 DOI: 10.1142/s0218202521500081
J. Carrillo, Young-Pil Choi, Jinwook Jung
In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the hydrodynamic limit of a kinetic Cucker--Smale flocking model with confinement, nonlocal interaction, and local alignment forces, linear damping and diffusion in velocity. We first discuss the hydrodynamic limit of our main equation under strong local alignment and diffusion regime, and we rigorously derive the isothermal Euler equations with nonlocal forces. We also analyze the hydrodynamic limit corresponding to strong local alignment without diffusion. In this case, the limiting system is pressureless Euler-type equations. Our analysis includes the Coulombian interaction potential for both cases and explicit estimates on the distance towards the limiting hydrodynamic equations. The relative entropy method is the crucial technology in our main results, however, for the case without diffusion, we combine a modulated macroscopic kinetic energy with the bounded Lipschitz distance to deal with the nonlocality in the interaction forces. For the sake of completeness, the existence of weak and strong solutions to the kinetic and fluid equations are also established.
在本文中,我们量化了数学生物学中出现的集体行为动力学方程的渐近极限,这些方程由具有非局部相互作用力和对准的vlasov型方程建模。更准确地说,我们研究了具有约束、非局部相互作用、局部对准力、线性阻尼和速度扩散的动态Cucker- small群集模型的水动力极限。我们首先讨论了在强局部对准和扩散条件下主方程的水动力极限,并严格推导了具有非局部力的等温欧拉方程。本文还分析了无扩散的强局部对准所对应的水动力极限。在这种情况下,极限系统是无压欧拉型方程。我们的分析包括两种情况下的库仑相互作用势和到极限流体动力方程的距离的显式估计。相对熵法是我们主要结果的关键技术,然而,对于没有扩散的情况,我们将调制宏观动能与有界Lipschitz距离结合起来处理相互作用力的非局域性。为完整起见,还建立了动力学方程和流体方程弱解和强解的存在性。
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引用次数: 12
The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation 无粘曲面拟地转方程经典解的寿命
Pub Date : 2020-07-09 DOI: 10.1016/J.ANIHPC.2020.12.005
'Angel Castro, D. C'ordoba, Fan Zheng
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引用次数: 4
期刊
arXiv: Analysis of PDEs
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