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Communications in Partial Differential Equations最新文献

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Slow periodic homogenization for Hamilton–jacobi equations Hamilton–jacobi方程的慢周期均匀化
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2023-02-03 DOI: 10.1080/03605302.2023.2246194
William Cooperman
{"title":"Slow periodic homogenization for Hamilton–jacobi equations","authors":"William Cooperman","doi":"10.1080/03605302.2023.2246194","DOIUrl":"https://doi.org/10.1080/03605302.2023.2246194","url":null,"abstract":"Abstract Capuzzo-Dolcetta–Ishii proved that the rate of periodic homogenization for coercive Hamilton–Jacobi equations is . We complement this result by constructing examples of coercive nonconvex Hamiltonians whose rate of periodic homogenization is .","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42808957","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
Erratum: the Poisson equation involving surface measures 勘误: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 : 2023-01-11 DOI: 10.1080/03605302.2022.2164303
Marius Müller
{"title":"Erratum: the Poisson equation involving surface measures","authors":"Marius Müller","doi":"10.1080/03605302.2022.2164303","DOIUrl":"https://doi.org/10.1080/03605302.2022.2164303","url":null,"abstract":"Abstract This erratum points out an error in “The Poisson equation involving surface measures” (Vol. 47 of Communications in Partial Differential Equations, (2022)) and provides a counterexample and discussion of the erroneous theorem.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42933567","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: 1
Homogenization of some periodic Hamilton-Jacobi equations with defects 一类有缺陷的周期Hamilton-Jacobi方程的齐化
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-11-29 DOI: 10.1080/03605302.2023.2238953
Y. Achdou, Claude Le Bris
{"title":"Homogenization of some periodic Hamilton-Jacobi equations with defects","authors":"Y. Achdou, Claude Le Bris","doi":"10.1080/03605302.2023.2238953","DOIUrl":"https://doi.org/10.1080/03605302.2023.2238953","url":null,"abstract":"Abstract We study homogenization for a class of stationary Hamilton-Jacobi equations in which the Hamiltonian is obtained by perturbing near the origin an otherwise periodic Hamiltonian. We prove that the limiting problem consists of a Hamilton-Jacobi equation outside the origin, with the same effective Hamiltonian as in periodic homogenization, supplemented at the origin with an effective Dirichlet condition that keeps track of the perturbation. Various comments and extensions are discussed.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43912390","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
Hyperbolic–parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion 不完全扩散交叉扩散系统的双曲-抛物范式和局部经典解
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-10-31 DOI: 10.1080/03605302.2023.2212479
P. Druet, Katharina Hopf, A. Jüngel
{"title":"Hyperbolic–parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion","authors":"P. Druet, Katharina Hopf, A. Jüngel","doi":"10.1080/03605302.2023.2212479","DOIUrl":"https://doi.org/10.1080/03605302.2023.2212479","url":null,"abstract":"Abstract We investigate degenerate cross-diffusion equations, with a rank-deficient diffusion-matrix, modelling multispecies population dynamics driven by partial pressure gradients. These equations have recently been found to arise in a mean-field limit of interacting stochastic particle systems. To date, their analysis in multiple space dimensions has been confined to the purely convective case with equal mobility coefficients. In this article, we introduce a normal form for an entropic class of such equations which reveals their structure of a symmetric hyperbolic–parabolic system. Due to the state-dependence of the range and kernel of the singular diffusive matrix, our way of rewriting the equations is different from that classically used for symmetric second-order systems with a nullspace invariance property. By means of this change of variables, we solve the Cauchy problem for short times and positive initial data in for","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45966347","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
Toward uniform existence and convergence theorems for three-scale systems of hyperbolic PDEs with general initial data 具有一般初始数据的三尺度双曲型偏微分方程组的一致存在性和收敛性定理
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-10-25 DOI: 10.1080/03605302.2022.2129383
S. Schochet, Xin Xu
{"title":"Toward uniform existence and convergence theorems for three-scale systems of hyperbolic PDEs with general initial data","authors":"S. Schochet, Xin Xu","doi":"10.1080/03605302.2022.2129383","DOIUrl":"https://doi.org/10.1080/03605302.2022.2129383","url":null,"abstract":"Abstract Uniform existence of solutions to initial-value problems and convergence of appropriately filtered solutions are proven for a special class of three-scale singular limit equations, without any restriction on the initial data. The uniform existence is proven using a novel system of energy estimates. The convergence result is based on a detailed analysis of the fastest-scale oscillations, which unlike in two-scale systems have no explicit solution formula.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45054278","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: 1
Taxis-driven persistent localization in a degenerate Keller-Segel system 退化Keller-Segel系统中出租车驱动的持续定位
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-10-18 DOI: 10.1080/03605302.2022.2122836
A. Stevens, M. Winkler
{"title":"Taxis-driven persistent localization in a degenerate Keller-Segel system","authors":"A. Stevens, M. Winkler","doi":"10.1080/03605302.2022.2122836","DOIUrl":"https://doi.org/10.1080/03605302.2022.2122836","url":null,"abstract":"Abstract The degenerate Keller-Segel type system is considered in balls with R > 0 and m > 1. Our main results reveal that throughout the entire degeneracy range the interplay between degenerate diffusion and cross-diffusive attraction herein can enforce persistent localization of solutions inside a compact subset of Ω, no matter whether solutions remain bounded or blow up. More precisely, it is shown that for arbitrary and one can find such that if and is nonnegative and radially symmetric with and then a corresponding zero-flux type initial-boundary value problem admits a radial weak solution (u, v), extensible up to a maximal time and satisfying if which has the additional property that In particular, this conclusion is seen to be valid whenever u 0 is radially nonincreasing with","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59338677","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
Recovery of a spatially-dependent coefficient from the NLS scattering map 从NLS散射图中恢复空间相关系数
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-09-16 DOI: 10.1080/03605302.2023.2241546
Jason Murphy
{"title":"Recovery of a spatially-dependent coefficient from the NLS scattering map","authors":"Jason Murphy","doi":"10.1080/03605302.2023.2241546","DOIUrl":"https://doi.org/10.1080/03605302.2023.2241546","url":null,"abstract":"Abstract We follow up on work of Strauss, Weder, and Watanabe concerning scattering and inverse scattering for nonlinear Schrödinger equations with nonlinearities of the form .","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46557667","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: 4
Green’s function of heat equation for heterogeneous media in 3-D 三维非均匀介质热方程的格林函数
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-09-08 DOI: 10.1080/03605302.2022.2116717
C. Cheng, Tai-Ping Liu, Shih-Hsien Yu
{"title":"Green’s function of heat equation for heterogeneous media in 3-D","authors":"C. Cheng, Tai-Ping Liu, Shih-Hsien Yu","doi":"10.1080/03605302.2022.2116717","DOIUrl":"https://doi.org/10.1080/03605302.2022.2116717","url":null,"abstract":"Abstract The purpose of the present paper is to study the structure of Green’s function for heat equation in several spatial dimensions and with rough heat conductivity coefficient. We take the heat conductivity coefficient to be of bounded variation in the x direction and study the dispersion in the (y, z) direction. The goal is to understand the coupling of dissipation across rough heat conductivity and the multi-dimensional dispersion in the Green’s function A series of exponential functions of path integral with coefficients over a field of complex analytic functions around imaginary axis are formulated in the Laplace and Fourier transforms variables. The Green’s function in the transformed variables is written as the sum of these integrals over random paths. The integral over a random path is rearranged through the reflection property over a variation of heat conductivity coefficient and become a simple form in terms of path phase and amplitude. The complex analytic and combinatorics method is then used to yield a precise pointwise structure of the Green’s function in the physical domain","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48161808","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
Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system 磁化Vlasov-Poisson系统的速度矩传播和唯一性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-09-07 DOI: 10.1080/03605302.2023.2175218
Alexandre Rege
{"title":"Propagation of velocity moments and uniqueness for the magnetized Vlasov–Poisson system","authors":"Alexandre Rege","doi":"10.1080/03605302.2023.2175218","DOIUrl":"https://doi.org/10.1080/03605302.2023.2175218","url":null,"abstract":"Abstract We present two results regarding the three-dimensional Vlasov–Poisson system in the full space with an external magnetic field. First, we investigate the propagation of velocity moments for solutions to the system when the magnetic field is uniform and time-dependent. We combine the classical moment approach with an induction procedure depending on the cyclotron period This allows us to obtain, like in the unmagnetized case, the propagation of velocity moments of order k > 2 in the full space case and of order k > 3 in the periodic case. Second, this time taking a general magnetic field that depends on both time and position, we manage to extend a result by Miot [A uniqueness criterion for unbounded solutions to the Vlasov–Poisson system, 2016] regarding uniqueness for Vlasov–Poisson to the magnetized framework.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45841889","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
Threshold solutions for the 3d cubic-quintic NLS 三维三次五次NLS的阈值解
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2022-08-17 DOI: 10.1080/03605302.2023.2212477
Alex H. Ardila, Jason Murphy
{"title":"Threshold solutions for the 3d cubic-quintic NLS","authors":"Alex H. Ardila, Jason Murphy","doi":"10.1080/03605302.2023.2212477","DOIUrl":"https://doi.org/10.1080/03605302.2023.2212477","url":null,"abstract":"Abstract We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and by certain rescalings thereof. We classify the possible behaviors of solutions on the part of the boundary attained solely by solitons. In particular, we show that non-soliton solutions either scatter in both time directions or coincide (modulo symmetries) with a special solution, which scatters in one time direction and converges exponentially to the soliton in the other.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42435389","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
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