Communications in Partial Differential Equations最新文献_第3页

Nonlinear enhanced dissipation in viscous Burgers type equations II 粘性Burgers型方程的非线性增强耗散II

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2023-11-14 DOI: 10.1080/03605302.2023.2277453

Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie

引用次数: 0

Monotone solutions for mean field games master equations: continuous state space and common noise 平均场博弈主方程的单调解:连续状态空间和共噪声

2区数学

Communications in Partial Differential Equations Pub Date : 2023-11-08 DOI: 10.1080/03605302.2023.2276564

Charles Bertucci

引用次数: 18

Asymptotics and scattering for wave Klein-Gordon systems 波Klein-Gordon系统的渐近性和散射

2区数学

Communications in Partial Differential Equations Pub Date : 2023-09-02 DOI: 10.1080/03605302.2023.2263205

Xuantao Chen, Hans Lindblad

{"title":"Asymptotics and scattering for wave Klein-Gordon systems","authors":"Xuantao Chen, Hans Lindblad","doi":"10.1080/03605302.2023.2263205","DOIUrl":"https://doi.org/10.1080/03605302.2023.2263205","url":null,"abstract":"AbstractWe study the coupled wave-Klein-Gordon systems, introduced by LeFloch-Ma and then Ionescu-Pausader, to model the nonlinear effects from the Einstein-Klein-Gordon equation in harmonic coordinates. We first go over a slightly simplified version of global existence based on LeFloch-Ma, and then derive the asymptotic behavior of the system. The asymptotics of the Klein-Gordon field consist of a modified phase times a homogeneous function, and the asymptotics of the wave equation consist of a radiation field in the wave zone and an interior homogeneous solution coupled to the Klein-Gordon asymptotics. We then consider the inverse problem, the scattering from infinity. We show that given the type of asymptotic behavior at infinity, there exist solutions of the system that present the exact same behavior.KEYWORDS: AsymptoticsScattering from infinityWave-Klein-Gordon systems Notes1 In fact, u3 would be zero if we only consider the term ϕ02. The presence of u3 comes from the lower order terms in (∂tϕ0)2.2 We use the Einstein summation convention. Also, when the repeated index is spatial, we define the expression to be the sum regardless of whether it is upper or lower, as the spatial part of the Minkowski metric is Euclidean.3 Here we use the decay |△yϕ|≲ερ−32+δ(1−|y|2)74−δ, for which we only have it with 47 replaced by 45 at this stage, but this can also be shown by dealing with commutators like the existence proof.4 Recall in Lemma 4.5, we require that α cannot be too worse. i.e. close to –1. However, once α satisfies this condition, the value of α does not affect the outcome of the estimate.5 Note that here we take the contribution from (∂tϕ)2 into account, which we did not consider in the introduction part for simplicity.Additional informationFundingH.L. was supported in part by Simons Collaboration Grant 638955. X.C. thanks Junfu Yao for helpful discussions.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134969703","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: 2

Synchronization in a Kuramoto mean field game Kuramoto平均场博弈中的同步

2区数学

Communications in Partial Differential Equations Pub Date : 2023-09-02 DOI: 10.1080/03605302.2023.2264611

Rene Carmona, Quentin Cormier, H. Mete Soner

引用次数: 6

A Globally Stable Self-Similar Blowup Profile in Energy Supercritical Yang-Mills Theory 能量超临界Yang-Mills理论的全局稳定自相似爆破剖面

2区数学

Communications in Partial Differential Equations Pub Date : 2023-09-02 DOI: 10.1080/03605302.2023.2263208

Roland Donninger, Matthias Ostermann

引用次数: 8

Qualitative properties of solutions to a mass-conserving free boundary problem modeling cell polarization 细胞极化的守恒质量自由边界问题解的定性性质

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2023-08-03 DOI: 10.1080/03605302.2023.2247467

Anna Logioti, B. Niethammer, Matthias Röger, J. Velázquez

引用次数: 0

Correction to: Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations 更正：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 : 2023-05-31 DOI: 10.1080/03605302.2023.2215296

Hui Chen, Tai-Peng Tsai, Ting Zhang

引用次数: 0

Erratum to “optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation” “一维Cahn–Hilliard方程类凸点解的最优松弛”勘误表

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2023-05-04 DOI: 10.1080/03605302.2023.2202732

S. Biesenbach, R. Schubert, Maria G. Westdickenberg

引用次数: 0

Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory 具有势的二维椭圆型方程的可观测性代价不等式及其在控制理论中的应用

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2023-04-03 DOI: 10.1080/03605302.2023.2190526

S. Ervedoza, K. L. Balc'h

{"title":"Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory","authors":"S. Ervedoza, K. L. Balc'h","doi":"10.1080/03605302.2023.2190526","DOIUrl":"https://doi.org/10.1080/03605302.2023.2190526","url":null,"abstract":"Abstract The goal of this article is to obtain observability estimates for non-homogeneous elliptic equations in the presence of a potential, posed on a smooth bounded domain Ω in and observed from a non-empty open subset More precisely, for our main result shows that, when has a finite number of holes, the observability constant of the elliptic operator with domain is of the form where C is a positive constant depending only on Ω and ω. Our methodology of proof is crucially based on the one recently developed by Logunov, Malinnikova, Nadirashvili, and Nazarov [1], in the context of the Landis conjecture on exponential decay of solutions to homogeneous elliptic equations in the plane The main difference and additional difficulty compared to [1] is that the zero set of the solutions to elliptic equations with source term can be very intricate and should be dealt with carefully. As a consequence of these new observability estimates, we obtain new results concerning control of semi-linear elliptic equations in the spirit of Fernández-Cara, Zuazua’s open problem concerning small-time global null-controllability of slightly super-linear heat equations.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42972923","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: 0

Maximal speed of quantum propagation for the Hartree equation Hartree方程量子传播的最大速度

IF 1.9 2区数学

Communications in Partial Differential Equations Pub Date : 2023-02-21 DOI: 10.1080/03605302.2023.2183408

J. Arbunich, J. Faupin, F. Pusateri, I. Sigal

引用次数: 4