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The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect 由带漂移的退化波方程控制的、热传导条件下带记忆效应的传输系统的能量衰减率
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300571
Mohammad Akil, Genni Fragnelli, Ibtissam Issa
{"title":"The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect","authors":"Mohammad Akil, Genni Fragnelli, Ibtissam Issa","doi":"10.1002/mana.202300571","DOIUrl":"https://doi.org/10.1002/mana.202300571","url":null,"abstract":"In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type . Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Local and global solutions on arcs for the Ericksen–Leslie problem in RN$mathbb {R}^N$ RN$mathbb {R}^N$ 中埃里克森-莱斯利问题弧上的局部和全局解
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300253
Daniele Barbera, Vladimir Georgiev
{"title":"Local and global solutions on arcs for the Ericksen–Leslie problem in RN$mathbb {R}^N$","authors":"Daniele Barbera, Vladimir Georgiev","doi":"10.1002/mana.202300253","DOIUrl":"https://doi.org/10.1002/mana.202300253","url":null,"abstract":"The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space with . In our work, we suppose the initial condition stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution <jats:disp-formula/><jats:disp-formula/>for , asking low regularity assumptions on and .","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Cauchy problem for a two‐component higher order Camassa–Holm system 关于双分量高阶卡马萨-霍姆系统的考奇问题
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300382
Shouming Zhou, Luhang Zhou, Rong Chen
{"title":"On the Cauchy problem for a two‐component higher order Camassa–Holm system","authors":"Shouming Zhou, Luhang Zhou, Rong Chen","doi":"10.1002/mana.202300382","DOIUrl":"https://doi.org/10.1002/mana.202300382","url":null,"abstract":"In this paper, we focus on the well‐posedness, blow‐up phenomena, and continuity of the data‐to‐solution map of the Cauchy problem for a two‐component higher order Camassa–Holm (CH) system. The local well‐posedness is established in Besov spaces with , which improves the local well‐posedness result proved before in Tang and Liu [Z. Angew. Math. Phys. 66 (2015), 1559–1580], Ye and Yin [arXiv preprint arXiv:2109.00948 (2021)], Zhang and Li [Nonlinear Anal. Real World Appl. 35 (2017), 414–440], and Zhou [Math. Nachr. 291 (2018), no. 10, 1595–1619]. Next, we consider the continuity of the solution‐to‐data map, that is, the ill‐posedness is derived in Besov space with and . Then, the nonuniform continuous and Hölder continuous dependence on initial data for this system are also presented in Besov spaces with and . Finally, the precise blow‐up criteria for the strong solutions of the two‐component higher order CH system is determined in the lowest Sobolev space with , which improves the blow‐up criteria result established before in He and Yin [Discrete Contin. Dyn. Syst. 37 (2016), no. 3, 1509–1537] and Zhou [Math. Nachr. 291 (2018), no. 10, 1595–1619].","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
(1,p)$(1,p)$‐Sobolev spaces based on strongly local Dirichlet forms 基于强局部 Dirichlet 形式的 (1,p)$(1,p)$-Sobolev 空间
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202400025
Kazuhiro Kuwae
{"title":"(1,p)$(1,p)$‐Sobolev spaces based on strongly local Dirichlet forms","authors":"Kazuhiro Kuwae","doi":"10.1002/mana.202400025","DOIUrl":"https://doi.org/10.1002/mana.202400025","url":null,"abstract":"In the framework of quasi‐regular strongly local Dirichlet form on admitting minimal ‐dominant measure , we construct a natural ‐energy functional on and ‐Sobolev space for . In this paper, we establish the Clarkson‐type inequality for . As a consequence, is a uniformly convex Banach space, hence it is reflexive. Based on the reflexivity of , we prove that (generalized) normal contraction operates on , which has been shown in the case of various concrete settings, but has not been proved for such a general framework. Moreover, we prove that ‐capacity for open set admits an equilibrium potential with ‐a.e. and ‐a.e. on .","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundedness in a quasilinear forager–exploiter model 准线性觅食者--开发者模型中的有界性
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300507
Jianping Wang, Qianying Zhang
{"title":"Boundedness in a quasilinear forager–exploiter model","authors":"Jianping Wang, Qianying Zhang","doi":"10.1002/mana.202300507","DOIUrl":"https://doi.org/10.1002/mana.202300507","url":null,"abstract":"We study a forager–exploiter model with nonlinear diffusions: <jats:disp-formula/>where is a smooth bounded domain, is a nonnegative bounded function, satisfying <jats:disp-formula/>with some sufficiently large . Global‐in‐time solutions are established for corresponding Neumann initial‐boundary value problem.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the spectrum of the algebra of bounded‐type symmetric analytic functions on ℓ1$ell _1$ 论 ℓ1$ell _1$ 上有界型对称解析函数代数的谱
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300415
Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk
{"title":"On the spectrum of the algebra of bounded‐type symmetric analytic functions on ℓ1$ell _1$","authors":"Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk","doi":"10.1002/mana.202300415","DOIUrl":"https://doi.org/10.1002/mana.202300415","url":null,"abstract":"We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space . This is achieved after proving that on the analogous algebra for , , the radius function of any evaluation homomorphism , coincides with the norm of .","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Weighted Kato–Ponce inequalities for multiple factors 多因素加权卡托-庞斯不等式
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-22 DOI: 10.1002/mana.202300443
Sean Douglas, Loukas Grafakos
{"title":"Weighted Kato–Ponce inequalities for multiple factors","authors":"Sean Douglas, Loukas Grafakos","doi":"10.1002/mana.202300443","DOIUrl":"https://doi.org/10.1002/mana.202300443","url":null,"abstract":"In this paper, we establish a weighted Kato–Ponce inequality for factors in the endpoint case. Furthermore, we extend the validity of the Kato–Ponce inequality from the class of Schwartz functions to the broader class of functions living in a (weighted) fractional Sobolev space.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On differentiability of Sobolev functions with respect to the Sobolev norm 关于索波列函数与索波列规范的可微分性
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-22 DOI: 10.1002/mana.202300545
Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov
{"title":"On differentiability of Sobolev functions with respect to the Sobolev norm","authors":"Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov","doi":"10.1002/mana.202300545","DOIUrl":"https://doi.org/10.1002/mana.202300545","url":null,"abstract":"We study connections between the ‐differentiability and the ‐differentiability of Sobolev functions. We prove that ‐differentiability implies the ‐differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the ‐differentiability of Sobolev functions ‐almost everywhere.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model 随机二维 Cahn-Hilliard-Navier-Stokes 模型的 Wong-Zakai 近似值
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-20 DOI: 10.1002/mana.202400065
T. Tachim Medjo
{"title":"Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model","authors":"T. Tachim Medjo","doi":"10.1002/mana.202400065","DOIUrl":"https://doi.org/10.1002/mana.202400065","url":null,"abstract":"In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert‐valued Brownian motion and some adapted finite‐dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fractional operators with homogeneous kernel on the Calderón product of Morrey spaces 莫雷空间卡尔德龙积上具有同质核的分数算子
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-07-15 DOI: 10.1002/mana.202400043
Daniel Salim, Moch. Taufik Hakiki, Yoshihiro Sawano, Denny Ivanal Hakim, Muhamad Jamaludin
{"title":"Fractional operators with homogeneous kernel on the Calderón product of Morrey spaces","authors":"Daniel Salim,&nbsp;Moch. Taufik Hakiki,&nbsp;Yoshihiro Sawano,&nbsp;Denny Ivanal Hakim,&nbsp;Muhamad Jamaludin","doi":"10.1002/mana.202400043","DOIUrl":"10.1002/mana.202400043","url":null,"abstract":"<p>We investigate fractional operators with homogeneous kernel in Morrey spaces. In particular, we prove that fractional integral operators and fractional maximal operators with homogeneous kernel are bounded from the Calderón product of Morrey spaces to certain Morrey spaces. Our results can be seen as a generalization of a recent result on the relation between the boundedness of (classical) fractional operators and interpolation of Morrey spaces. What is new about this paper is not only the passage from the classical fractional integral operators to the rough integral operators. Even the case of fractional integral operators, handled in earlier papers, is significantly simplified.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141649264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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