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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
arXiv: Analysis of PDEs Pub Date : 2020-07-22 DOI: 10.1016/J.MATPUR.2021.07.010
Youjun Deng, Hongyu Liu, G. Zheng
{"title":"Mathematical analysis of plasmon resonances for curved nanorods","authors":"Youjun Deng, Hongyu Liu, G. Zheng","doi":"10.1016/J.MATPUR.2021.07.010","DOIUrl":"https://doi.org/10.1016/J.MATPUR.2021.07.010","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82035585","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: 19
Local Well Posedness of the Euler–Korteweg Equations on $${{mathbb {T}}^d}$$ 上Euler-Korteweg方程的局部适定性 $${{mathbb {T}}^d}$$
arXiv: Analysis of PDEs 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":null,"pages":null},"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
arXiv: Analysis of PDEs Pub Date : 2020-07-20 DOI: 10.1090/proc/15415
C. Sourdis
{"title":"A one-dimensional symmetry result for entire solutions to the Fisher-KPP equation","authors":"C. Sourdis","doi":"10.1090/proc/15415","DOIUrl":"https://doi.org/10.1090/proc/15415","url":null,"abstract":"We consider the Fisher-KPP reaction-diffusion equation in the whole space. \u0000We 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.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73201935","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-17 DOI: 10.1142/s0218202521500391
Karina Kowalczyk, Richard Hofer, S. Schwarzacher
{"title":"Darcy’s law as low Mach and homogenization limit of a compressible fluid in perforated domains","authors":"Karina Kowalczyk, Richard Hofer, S. Schwarzacher","doi":"10.1142/s0218202521500391","DOIUrl":"https://doi.org/10.1142/s0218202521500391","url":null,"abstract":"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 $gamma> frac32$.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85399720","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-16 DOI: 10.2422/2036-2145.201903_006
Edgard A. Pimentel, J. M. Urbano
{"title":"Existence and improved regularity for a nonlinear system with collapsing ellipticity","authors":"Edgard A. Pimentel, J. M. Urbano","doi":"10.2422/2036-2145.201903_006","DOIUrl":"https://doi.org/10.2422/2036-2145.201903_006","url":null,"abstract":"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.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86122803","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: 0
A triviality result for semilinear parabolic equations 半线性抛物方程的一个平凡结果
arXiv: Analysis of PDEs Pub Date : 2020-07-15 DOI: 10.3934/MINE.2022002
G. Catino, D. Castorina, C. Mantegazza
{"title":"A triviality result for semilinear parabolic equations","authors":"G. Catino, D. Castorina, C. Mantegazza","doi":"10.3934/MINE.2022002","DOIUrl":"https://doi.org/10.3934/MINE.2022002","url":null,"abstract":"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 $frac{n+2}{n-2}$.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79733908","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-14 DOI: 10.3934/DCDS.2021085
K. M. Hui, Jinwan Park
{"title":"Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured euclidean space","authors":"K. M. Hui, Jinwan Park","doi":"10.3934/DCDS.2021085","DOIUrl":"https://doi.org/10.3934/DCDS.2021085","url":null,"abstract":"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 $nge 3$, $0<m<frac{n-2}{n}$, $beta<0$ and $alpha=frac{2beta}{1-m}$, we prove the existence and asymptotic behaviour of singular eternal self-similar solution of the fast diffusion equation. As a consequence, we prove the existence and uniqueness of solution of Cauchy problem for the fast diffusion equation. For $n=3, 4$ and $frac{n-2}{n+2}le m 0$. Furthermore, for the radially symmetric initial value $u_0$, $3 le n < 8$, $1- sqrt{frac{2}{n}} le m le min left {frac{2(n-2)}{3n}, frac{n-2}{n+2}right }$, we also have the asymptotic large time behaviour.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83672243","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-13 DOI: 10.1016/J.NONRWA.2021.103410
Young-Pil Choi, K. Kang, Hwa Kil Kim, Jae‐Myoung Kim
{"title":"Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow","authors":"Young-Pil Choi, K. Kang, Hwa Kil Kim, Jae‐Myoung Kim","doi":"10.1016/J.NONRWA.2021.103410","DOIUrl":"https://doi.org/10.1016/J.NONRWA.2021.103410","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72828054","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-09 DOI: 10.1142/s0218202521500081
J. Carrillo, Young-Pil Choi, Jinwook Jung
{"title":"Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces","authors":"J. Carrillo, Young-Pil Choi, Jinwook Jung","doi":"10.1142/s0218202521500081","DOIUrl":"https://doi.org/10.1142/s0218202521500081","url":null,"abstract":"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.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89464798","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: 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
arXiv: Analysis of PDEs Pub Date : 2020-07-09 DOI: 10.1016/J.ANIHPC.2020.12.005
'Angel Castro, D. C'ordoba, Fan Zheng
{"title":"The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation","authors":"'Angel Castro, D. C'ordoba, Fan Zheng","doi":"10.1016/J.ANIHPC.2020.12.005","DOIUrl":"https://doi.org/10.1016/J.ANIHPC.2020.12.005","url":null,"abstract":"","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77206612","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
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