{"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}
{"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
{"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}