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Communications on Pure and Applied Analysis最新文献

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Fourth-order operators with unbounded coefficients 系数无界的四阶算子
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2024-01-25 DOI: 10.3934/cpaa.2024020
Federica Gregorio, Chiara Spina, C. Tacelli
{"title":"Fourth-order operators with unbounded coefficients","authors":"Federica Gregorio, Chiara Spina, C. Tacelli","doi":"10.3934/cpaa.2024020","DOIUrl":"https://doi.org/10.3934/cpaa.2024020","url":null,"abstract":"We prove that operators of the form $A=-a(x)^2Delta^{2}$, with $|D a(x)|leq c a(x)^frac{1}{2}$, generate analytic semigroups in $L^p(mathbb{R}^N)$ for $1<pleqinfty$ and in $C_b(mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^{alpha} Delta^{2}$, $0leqalphaleq2$. Moreover, we characterize the maximal domain of such operators in $L^p(mathbb{R}^N)$ for $1<p<infty$.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140495530","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
The Dirac bag model in strong magnetic fields 强磁场下的狄拉克袋模型
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-08-24 DOI: 10.2140/paa.2023.5.643
J. Barbaroux, L. Le Treust, N. Raymond, E. Stockmeyer
{"title":"The Dirac bag model in strong magnetic fields","authors":"J. Barbaroux, L. Le Treust, N. Raymond, E. Stockmeyer","doi":"10.2140/paa.2023.5.643","DOIUrl":"https://doi.org/10.2140/paa.2023.5.643","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90357090","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
The Alexandroff–Bakelman–Pucci estimate viapositive drift 亚历山德罗夫-贝克曼-普奇估计通过正漂移
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-06-26 DOI: 10.2140/paa.2023.5.261
A. Vitolo
{"title":"The Alexandroff–Bakelman–Pucci estimate via\u0000positive drift","authors":"A. Vitolo","doi":"10.2140/paa.2023.5.261","DOIUrl":"https://doi.org/10.2140/paa.2023.5.261","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76150459","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 analysis for 1D compressible Navier-Stokes-Vlasov equations 一维可压缩Navier-Stokes-Vlasov方程的渐近分析
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-02-01 DOI: 10.3934/cpaa.2020119
Xinran Shi, Yunfei Su, Lei Yao
{"title":"Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations","authors":"Xinran Shi, Yunfei Su, Lei Yao","doi":"10.3934/cpaa.2020119","DOIUrl":"https://doi.org/10.3934/cpaa.2020119","url":null,"abstract":"We consider the initial-boundary value problem of compressible Navier–Stokes–Vlasov equations under a local alignment regime in a one-dimensional bounded domain. Based on the relative entropy method and compactness argument, we prove that a weak solution of the initial-boundary value problem converges to a strong solution of the limiting two-phase fluid system. This work extends in some sense the previous work of Choi and Jung [Math. Models Methods Appl. Sci. 31(11), 2213–2295 (2021)], which considered the diffusive term ∂ ξξ f ɛ in the kinetic equation. Note that the diffusion term was not considered in this paper.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80921587","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
A Courant nodal domain theorem for linearized mean field type equations 线性化平均场型方程的一个Courant节点域定理
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-22 DOI: 10.3934/cpaa.2023085
D. Bartolucci, Aleks Jevnikar, Ruijun Wu
{"title":"A Courant nodal domain theorem for linearized mean field type equations","authors":"D. Bartolucci, Aleks Jevnikar, Ruijun Wu","doi":"10.3934/cpaa.2023085","DOIUrl":"https://doi.org/10.3934/cpaa.2023085","url":null,"abstract":"We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42482210","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
Initial-boundary value problems to semilinear multi-term fractional differential equations 半线性多项分式微分方程的初边值问题
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-18 DOI: 10.3934/cpaa.2023068
S. Siryk, Nataliya Vasylyeva
{"title":"Initial-boundary value problems to semilinear multi-term fractional differential equations","authors":"S. Siryk, Nataliya Vasylyeva","doi":"10.3934/cpaa.2023068","DOIUrl":"https://doi.org/10.3934/cpaa.2023068","url":null,"abstract":"For $nu,nu_i,mu_jin(0,1)$, we analyze the semilinear integro-differential equation on the one-dimensional domain $Omega=(a,b)$ in the unknown $u=u(x,t)$ [ mathbf{D}_{t}^{nu}(varrho_{0}u)+sum_{i=1}^{M}mathbf{D}_{t}^{nu_{i}}(varrho_{i}u) -sum_{j=1}^{N}mathbf{D}_{t}^{mu_{j}}(gamma_{j}u) -mathcal{L}_{1}u-mathcal{K}*mathcal{L}_{2}u+f(u)=g(x,t), ] where $mathbf{D}_{t}^{nu},mathbf{D}_{t}^{nu_{i}}, mathbf{D}_{t}^{mu_{j}}$ are Caputo fractional derivatives, $varrho_0=varrho_0(t)>0,$ $varrho_{i}=varrho_{i}(t)$, $gamma_{j}=gamma_{j}(t)$, $mathcal{L}_{k}$ are uniform elliptic operators with time-dependent smooth coefficients, $mathcal{K}$ is a summable convolution kernel. Particular cases of this equation are the recently proposed advanced models of oxygen transport through capillaries. Under certain structural conditions on the nonlinearity $f$ and orders $nu,nu_i,mu_j$, the global existence and uniqueness of classical and strong solutions to the related initial-boundary value problems are established via the so-called continuation arguments method. The crucial point is searching suitable a priori estimates of the solution in the fractional H\"{o}lder and Sobolev spaces. The problems are also studied from the numerical point of view.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46481739","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 a diffusion model for growth and dispersal in a population 关于种群生长和扩散的扩散模型
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023025
G. Coclite, L. Ruvo
{"title":"On a diffusion model for growth and dispersal in a population","authors":"G. Coclite, L. Ruvo","doi":"10.3934/cpaa.2023025","DOIUrl":"https://doi.org/10.3934/cpaa.2023025","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":"70221144","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
Threshold dynamics of an age-space structure vector-borne disease model with multiple transmission pathways 具有多重传播途径的年龄空间结构病媒传播模型的阈值动力学
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023035
Yangyang Shi, Hongyong Zhao, Xuebing Zhang
{"title":"Threshold dynamics of an age-space structure vector-borne disease model with multiple transmission pathways","authors":"Yangyang Shi, Hongyong Zhao, Xuebing Zhang","doi":"10.3934/cpaa.2023035","DOIUrl":"https://doi.org/10.3934/cpaa.2023035","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":"70221162","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: 3
Interfaces with boundary intersection for an inhomogeneous Allen-Cahn equation in three-dimensional case 三维非齐次Allen-Cahn方程的边界交界面
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023039
Qiang Ren, Bin Xu
{"title":"Interfaces with boundary intersection for an inhomogeneous Allen-Cahn equation in three-dimensional case","authors":"Qiang Ren, Bin Xu","doi":"10.3934/cpaa.2023039","DOIUrl":"https://doi.org/10.3934/cpaa.2023039","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":"70221275","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 sublinear singular (p, q) Laplacian problems 次线性奇异(p, q)拉普拉斯问题
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023087
B. Alreshidi, D. D. Hai, R. Shivaji
{"title":"On sublinear singular (p, q) Laplacian problems","authors":"B. Alreshidi, D. D. Hai, R. Shivaji","doi":"10.3934/cpaa.2023087","DOIUrl":"https://doi.org/10.3934/cpaa.2023087","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":"70221489","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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