Communications in Partial Differential Equations最新文献_第6页

Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem 弹性系统的定量唯一延拓及其在运动学逆破裂问题中的应用

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-03-25 DOI: 10.1080/03605302.2023.2175215

M. V. de Hoop, M. Lassas, Jinpeng Lu, L. Oksanen

引用次数: 2

On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds 关于广义Aviles-Giga-泛函：紧致性、零能态、正则性估计和能量界

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-03-10 DOI: 10.1080/03605302.2022.2118609

X. Lamy, A. Lorent, G. Peng

引用次数: 3

Segregated solutions for nonlinear Schrödinger systems with weak interspecies forces 具有弱种间力的非线性Schrödinger系统的分离解

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-03-03 DOI: 10.1080/03605302.2022.2109488

A. Pistoia, Giusi Vaira

引用次数: 8

Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations Zvonkin变换与椭圆型方程解的正则性

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-03-02 DOI: 10.1080/03605302.2022.2139724

V. Bogachev, M. Röckner, S. V. Shaposhnikov

引用次数: 4

Analysis of the generalized Aw-Rascle model 广义Aw-Rascle模型的分析

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-02-08 DOI: 10.1080/03605302.2023.2183511

N. Chaudhuri, P. Gwiazda, E. Zatorska

引用次数: 1

The Poisson equation involving surface measures 涉及表面测度的泊松方程

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-01-11 DOI: 10.1080/03605302.2021.2013882

Marius Müller

引用次数: 2

Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations 关于三维Navier-Stokes方程轴对称解的局部正则性的注记

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2022-01-05 DOI: 10.1080/03605302.2022.2070854

Hui Chen, Tai-Peng Tsai, Ting Zhang

引用次数: 7

Propagation of chaos for the Cucker-Smale systems under heavy tail communication 重尾通信条件下cucker -小系统混沌的传播

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-12-08 DOI: 10.1080/03605302.2022.2091454

V. Nguyen, R. Shvydkoy

{"title":"Propagation of chaos for the Cucker-Smale systems under heavy tail communication","authors":"V. Nguyen, R. Shvydkoy","doi":"10.1080/03605302.2022.2091454","DOIUrl":"https://doi.org/10.1080/03605302.2022.2091454","url":null,"abstract":"Abstract In this work, we study propagation of chaos for solutions of the Liouville equation derived from the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies the heavy tail condition – known to be necessary to induce exponential alignment – we obtain a linear in time convergence rate of the k-th marginals to the product of k solutions of the corresponding Vlasov-Alignment equation, Specifically, the following estimate holds in terms of Wasserstein-2 metric (1) For systems with the Rayleigh-type friction and self-propulsion force, we obtain a similar result for sectorial solutions. Such solutions are known to align exponentially fast via the method of Grassmannian reduction. We recast the method in the kinetic setting and show that the bound (1) persists but with the quadratic dependence on time. In both the forceless and forced cases, the result represents an improvement over the exponential bounds established earlier in the work of Natalini and Paul, although those bounds hold for general kernels. The main message of our work is that flocking dynamics improves the rate considerably.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1883 - 1906"},"PeriodicalIF":1.9,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42782014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

A variational approach to first order kinetic mean field games with local couplings 具有局部耦合的一阶动力学平均场对策的变分方法

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-12-06 DOI: 10.1080/03605302.2022.2101003

Megan Griffin-Pickering, A. M'esz'aros

{"title":"A variational approach to first order kinetic mean field games with local couplings","authors":"Megan Griffin-Pickering, A. M'esz'aros","doi":"10.1080/03605302.2022.2101003","DOIUrl":"https://doi.org/10.1080/03605302.2022.2101003","url":null,"abstract":"Abstract First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results for the well-posedness theory of mean field games with control on the acceleration assume either that the running and final costs are regularizing functionals of the density variable, or the presence of noise, i.e. a second-order system. In this article we construct global in time weak solutions to a first order mean field games system involving kinetic transport operators, where the costs are local (hence non-regularizing) functions of the density variable with polynomial growth. We show the uniqueness of these solutions on the support of the agent density. This is achieved by characterizing solutions through two convex optimization problems in duality. As part of our approach, we develop tools for the analysis of mean field games on a non-compact domain by variational methods. We introduce a notion of ‘reachable set’, built from the initial measure, that allows us to work with initial measures with or without compact support. In this way we are able to obtain crucial estimates on minimizing sequences for merely bounded and continuous initial measures. These are then carefully combined with L 1-type averaging lemmas from kinetic theory to obtain pre-compactness for the minimizing sequence. Finally, under stronger convexity and monotonicity assumptions on the data, we prove higher order Sobolev estimates of the solutions.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1945 - 2022"},"PeriodicalIF":1.9,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49465388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

The Hele–Shaw flow as the sharp interface limit of the Cahn–Hilliard equation with disparate mobilities Hele–Shaw流作为具有不同迁移率的Cahn–Hilliard方程的尖锐界面极限

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2021-11-29 DOI: 10.1080/03605302.2022.2129384

Milan Kroemer, Tim Laux

引用次数: 6