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Communications on Pure and Applied Analysis最新文献

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Marcinkiewicz type operators with kernels involving Bessel functions 带有贝塞尔函数核的Marcinkiewicz型算子
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023086
Laith Hawawsheh, Ahmad Al-Salman
{"title":"Marcinkiewicz type operators with kernels involving Bessel functions","authors":"Laith Hawawsheh, Ahmad Al-Salman","doi":"10.3934/cpaa.2023086","DOIUrl":"https://doi.org/10.3934/cpaa.2023086","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221481","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
Asymptotic behavior for wave equations with space-dependent damping in a weighted energy class 具有空间相关阻尼的加权能量类波动方程的渐近行为
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023058
M. Sobajima
{"title":"Asymptotic behavior for wave equations with space-dependent damping in a weighted energy class","authors":"M. Sobajima","doi":"10.3934/cpaa.2023058","DOIUrl":"https://doi.org/10.3934/cpaa.2023058","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221512","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: 1
Random attractors for non-autonomous stochastic Navier-Stokes-Voigt equations in some unbounded domains 一些无界区域中非自治随机Navier-Stokes-Voigt方程的随机吸引子
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023062
Shu Wang, Mengmeng Si, Rong Yang
{"title":"Random attractors for non-autonomous stochastic Navier-Stokes-Voigt equations in some unbounded domains","authors":"Shu Wang, Mengmeng Si, Rong Yang","doi":"10.3934/cpaa.2023062","DOIUrl":"https://doi.org/10.3934/cpaa.2023062","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221574","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
Singular limits of invariant measures of the 3D MHD-Voigt equations 三维MHD-Voigt方程不变测度的奇异极限
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023116
Yuanyuan Zhang, Guanggan Chen
{"title":"Singular limits of invariant measures of the 3D MHD-Voigt equations","authors":"Yuanyuan Zhang, Guanggan Chen","doi":"10.3934/cpaa.2023116","DOIUrl":"https://doi.org/10.3934/cpaa.2023116","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135312070","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
Fourth order Hardy-Sobolev equations: Singularity and doubly critical exponent 四阶Hardy-Sobolev方程:奇点与双临界指数
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023112
Hussein Cheikh Ali
{"title":"Fourth order Hardy-Sobolev equations: Singularity and doubly critical exponent","authors":"Hussein Cheikh Ali","doi":"10.3934/cpaa.2023112","DOIUrl":"https://doi.org/10.3934/cpaa.2023112","url":null,"abstract":"In dimension $ Ngeq 5 $, and for $ 0< s<4 $ with $ gammain mathbb{R} $, we study the existence of nontrivial weak solutions for the doubly critical problem$ Delta^2 u-frac{gamma}{|x|^4}u = |u|^{2^star_0-2}u+frac{|u|^{ 2_s^{star}-2}u}{|x|^s}hbox{ in } mathbb{R}_+^N, ; u = Delta u = 0hbox{ on }partial mathbb{R}_+^N, $where $ 2_s^{star}: = frac{2(N-s)}{N-4} $ is the critical Hardy–Sobolev exponent. For $ Ngeq 8 $ and $ 0< gamma<frac{(N^2-4)^2}{16} $, we show the existence of nontrivial solution using the Mountain-Pass theorem by Ambrosetti-Rabinowitz. The method used is based on the existence of extremals for certain Hardy-Sobolev embeddings that we prove in this paper.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136366896","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
Coexistence of hyperbolic and elliptic invariant tori for completely degenerate quasi-periodically forced maps 完全退化拟周期强迫映射的双曲不变环面与椭圆不变环面共存
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023029
Guangzhao Zhou, Yehui Zhang, Wen Si
{"title":"Coexistence of hyperbolic and elliptic invariant tori for completely degenerate quasi-periodically forced maps","authors":"Guangzhao Zhou, Yehui Zhang, Wen Si","doi":"10.3934/cpaa.2023029","DOIUrl":"https://doi.org/10.3934/cpaa.2023029","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220694","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 weighted Dirichlet eigenvalues of Hardy operators involving critical gradient terms 涉及临界梯度项的Hardy算子的加权Dirichlet特征值
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023023
Ying Wang, Yanjing Qiu, Qingping Yin
{"title":"On the weighted Dirichlet eigenvalues of Hardy operators involving critical gradient terms","authors":"Ying Wang, Yanjing Qiu, Qingping Yin","doi":"10.3934/cpaa.2023023","DOIUrl":"https://doi.org/10.3934/cpaa.2023023","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221129","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 well-posedness and stability for a coupled nonlinear suspension bridge problem 耦合非线性悬索桥问题的适定性与稳定性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023084
S. E. Mukiawa, M. Leblouba, S. Messaoudi
{"title":"On the well-posedness and stability for a coupled nonlinear suspension bridge problem","authors":"S. E. Mukiawa, M. Leblouba, S. Messaoudi","doi":"10.3934/cpaa.2023084","DOIUrl":"https://doi.org/10.3934/cpaa.2023084","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221476","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
Mixed local and nonlocal supercritical Dirichlet problems 混合局部和非局部超临界狄利克雷问题
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023104
David Amundsen, Abbas Moameni, Remi Yvant Temgoua
{"title":"Mixed local and nonlocal supercritical Dirichlet problems","authors":"David Amundsen, Abbas Moameni, Remi Yvant Temgoua","doi":"10.3934/cpaa.2023104","DOIUrl":"https://doi.org/10.3934/cpaa.2023104","url":null,"abstract":"In this work, we consider a mixed local and nonlocal Dirichlet problem with supercritical nonlinearity. We first establish a multiplicity result for the problem $ begin{equation} Lu = |u|^{p-2}u+mu |u|^{q-2}uquadtext{in}; ; Omega, quadquad u = 0quadtext{in}; ; mathbb{R}^NsetminusOmega, ~~~(1) end{equation} $ where $ L: = -Delta +(-Delta)^s $ for $ sin(0, 1) $ and $ Omegasubsetmathbb{R}^N $ is a bounded domain. Precisely, we show that problem (1) for $ 1<q<2<p $ has a positive solution as well as a sequence of sign-changing solutions with a negative energy for small values of $ mu $. Here $ u $ can be either a scalar function, or a vector valued function so that (1) turns into a system with supercritical nonlinearity. Moreover, whenever the domain is symmetric, we also prove the existence of symmetric solutions enjoying the same symmetry properties. We shall also prove an existence result for the supercritical Hamiltonian system$ Lu = |v|^{p-2}v, qquad Lv = |u|^{d-2}u+mu |u|^{q-2}u $with the Dirichlet boundary condition on $ Omega $ where $ 1<q<2<p, d $. Our method is variational, and in both problems the lack of compactness for the supercritical problem is recovered by working on a closed convex subset of an appropriate function space.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496197","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: 2
A new type of stable shock formation in gas dynamics 气体动力学中一种新型稳定激波形成
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023118
Isaac Neal, Calum Rickard, Steve Shkoller, Vlad Vicol
{"title":"A new type of stable shock formation in gas dynamics","authors":"Isaac Neal, Calum Rickard, Steve Shkoller, Vlad Vicol","doi":"10.3934/cpaa.2023118","DOIUrl":"https://doi.org/10.3934/cpaa.2023118","url":null,"abstract":"From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form $ C^{0,nu} $ cusps as a first singularity, for any $ nu in [frac{1}{2}, 1) $. For this range of $ nu $, this is the first result demonstrating the stable formation of such $ C^{0,nu} $ cusp-type singularities, also known as pre-shocks. The proof uses a new formulation of the differentiated Euler equations along the fast acoustic characteristic, and relies on a novel set of $ L^p $ energy estimates for all $ 1<p<infty $, which may be of independent interest.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135604154","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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