{"title":"Convergence analysis for kernel-regularized online regression associated with an RRKHS","authors":"X. Pan, Lin Liu, B. Sheng","doi":"10.3934/cpaa.2023055","DOIUrl":"https://doi.org/10.3934/cpaa.2023055","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221438","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}
{"title":"On three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates with trapping potentials","authors":"Zhi-You Chen, Yu-Jen Huang, Yong Tang","doi":"10.3934/cpaa.2023056","DOIUrl":"https://doi.org/10.3934/cpaa.2023056","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221446","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}
{"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":"1 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
{"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":"1 1","pages":""},"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}
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
本文研究了一类具有超临界非线性的混合局部和非局部狄利克雷问题。我们首先建立了问题$ begin{equation} Lu = |u|^{p-2}u+mu |u|^{q-2}uquadtext{in}; ; Omega, quadquad u = 0quadtext{in}; ; mathbb{R}^NsetminusOmega, ~~~(1) end{equation} $的多重性结果，其中$ sin(0, 1) $和$ Omegasubsetmathbb{R}^N $的$ L: = -Delta +(-Delta)^s $是一个有界域。准确地说，我们证明了$ 1<q<2<p $的问题(1)有一个正解，以及对于$ mu $的小值具有负能量的换号解序列。这里$ u $可以是标量函数，也可以是矢量值函数，这样(1)就变成了一个具有超临界非线性的系统。此外，只要定义域是对称的，我们也证明了具有相同对称性的对称解的存在性。我们还证明了在$ Omega $上具有Dirichlet边界条件的超临界哈密顿系统$ Lu = |v|^{p-2}v, qquad Lv = |u|^{d-2}u+mu |u|^{q-2}u $的存在性结果，其中$ 1<q<2<p, d $。我们的方法是变分的，并且在这两个问题中，超临界问题的紧性缺失通过在适当函数空间的闭凸子集上工作来恢复。
{"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":"47 1","pages":"0"},"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}
Isaac Neal, Calum Rickard, Steve Shkoller, Vlad Vicol
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
从一个开放的初始数据集，我们构造了一维非等熵可压缩欧拉方程的经典解族，这些方程形成$ C^{0,nu} $顶点作为第一奇点，对于任何$ nu in [frac{1}{2}, 1) $。对于这个$ nu $范围，这是第一个证明这种$ C^{0,nu} $尖型奇点(也称为预冲击)稳定形成的结果。该证明使用了沿快速声学特性的微分欧拉方程的新公式，并依赖于所有$ 1<p<infty $的一组新的$ L^p $能量估计，这可能是独立的兴趣。
{"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":"4 1","pages":"0"},"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}
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