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Differential and Integral Equations最新文献

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Local uniform convergence and eventual positivity of solutions to biharmonic heat equations 双调和热方程解的局部一致收敛性和最终正性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-04 DOI: 10.57262/die036-0910-727
D. Daners, Jochen Gluck, J. Mui
{"title":"Local uniform convergence and eventual positivity of solutions to biharmonic heat equations","authors":"D. Daners, Jochen Gluck, J. Mui","doi":"10.57262/die036-0910-727","DOIUrl":"https://doi.org/10.57262/die036-0910-727","url":null,"abstract":"We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43501794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Uniqueness and continuous dependence for a viscoelastic problem with memory in domains with time dependent cracks 具有时间相关裂纹区域中具有记忆的粘弹性问题的唯一性和连续依赖性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-01 DOI: 10.57262/die034-1112-595
Federico Cianci, G. Dal Maso
{"title":"Uniqueness and continuous dependence for a viscoelastic problem with memory in domains with time dependent cracks","authors":"Federico Cianci, G. Dal Maso","doi":"10.57262/die034-1112-595","DOIUrl":"https://doi.org/10.57262/die034-1112-595","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44692570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Inhomogeneous Neumann-boundary value problem for nonlinear Schrödinger equations in the upper half-space 上半空间非线性Schrödinger方程的非齐次neumann边值问题
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-01 DOI: 10.57262/die034-1112-641
N. Hayashi, E. Kaikina, T. Ogawa
{"title":"Inhomogeneous Neumann-boundary value problem for nonlinear Schrödinger equations in the upper half-space","authors":"N. Hayashi, E. Kaikina, T. Ogawa","doi":"10.57262/die034-1112-641","DOIUrl":"https://doi.org/10.57262/die034-1112-641","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48255081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
A new Kirchhoff-Schrödinger-Poisson type system on the Heisenberg group 海森堡群上一个新的Kirchhoff-Schrödinger-Poisson型系统
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-01 DOI: 10.57262/die034-1112-621
Zeyi Liu, Deli Zhang
{"title":"A new Kirchhoff-Schrödinger-Poisson type system on the Heisenberg group","authors":"Zeyi Liu, Deli Zhang","doi":"10.57262/die034-1112-621","DOIUrl":"https://doi.org/10.57262/die034-1112-621","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44552762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4
Global existence for one-dimensional hyperbolic equation with power type nonlinearity 具有幂型非线性的一维双曲型方程的全局存在性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-11-01 DOI: 10.57262/die034-1112-675
Yutaka Tamada
{"title":"Global existence for one-dimensional hyperbolic equation with power type nonlinearity","authors":"Yutaka Tamada","doi":"10.57262/die034-1112-675","DOIUrl":"https://doi.org/10.57262/die034-1112-675","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41827770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 generalized parabolic Hardy-Hénon equation: Existence, blow-up, self-similarity and large-time asymptotic behavior 广义抛物型hardy - hsamnon方程的存在性、爆破性、自相似性和大时渐近性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-10-27 DOI: 10.57262/die035-0102-57
Gael Diebou Yomgne
{"title":"On the generalized parabolic Hardy-Hénon equation: Existence, blow-up, self-similarity and large-time asymptotic behavior","authors":"Gael Diebou Yomgne","doi":"10.57262/die035-0102-57","DOIUrl":"https://doi.org/10.57262/die035-0102-57","url":null,"abstract":"This paper deals with the Cauchy problem for the Hardy-Hénon equation (and its fractional analogue). Local well-posedness for initial data in the class of continuous functions with slow decay at infinity is investigated. Small data (in critical weak-Lebesgue space) global well-posedness is obtained in Cb([0,∞); L c(R)). As a direct consequence, global existence for data in strong critical Lebesgue Lc (R) follows under a smallness condition while uniqueness is unconditional. Besides, we prove the existence of self-similar solutions and examine the long time behavior of globally defined solutions. The zero solution u ≡ 0 is shown to be asymptotically stable in Lc (R) – it is the only self-similar solution which is initially small in Lc (R). Moreover, blow-up results are obtained under mild assumptions on the initial data and the corresponding Fujita critical exponent is found.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48199158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Well-posedness of the coagulation-fragmentation equation with size diffusion 具有尺寸扩散的混凝碎裂方程的适定性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-10-18 DOI: 10.57262/die035-0304-211
Philippe Laurencçot, Christoph Walker
{"title":"Well-posedness of the coagulation-fragmentation equation with size diffusion","authors":"Philippe Laurencçot, Christoph Walker","doi":"10.57262/die035-0304-211","DOIUrl":"https://doi.org/10.57262/die035-0304-211","url":null,"abstract":"describes the dynamics of the size distribution function φ = φ(t, x) ≥ 0 of particles of size x ∈ (0,∞) at time t > 0. Particles modify their sizes according to three different mechanisms: random fluctuations, here accounted for by size diffusion at a constant diffusion rate D > 0 (hereafter normalized toD = 1), spontaneous fragmentation with overall fragmentation rate a ≥ 0 and daughter distribution function b ≥ 0, and binary coalescence with coagulation kernel k ≥ 0. Nucleation is not taken into account in this model, an assumption which leads to the homogeneous Dirichlet boundary condition (1.1b) at x = 0. Let us recall that the coagulation-fragmentation equation without size diffusion, corresponding to setting D = 0 in (1.1a), arises in several fields of physics (grain growth, aerosol and raindrops formation, polymer and colloidal chemistry) and biology (hematology, animal grouping) and has been studied extensively in the mathematical literature since the pioneering works","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46636783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Zero energy critical points of functionals depending on a parameter 函数的零能量临界点取决于一个参数
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-09-02 DOI: 10.57262/die036-0506-413
H. R. Quoirin, Jefferson S. Silva, K. Silva
{"title":"Zero energy critical points of functionals depending on a parameter","authors":"H. R. Quoirin, Jefferson S. Silva, K. Silva","doi":"10.57262/die036-0506-413","DOIUrl":"https://doi.org/10.57262/die036-0506-413","url":null,"abstract":"We investigate zero energy critical points for a class of functionals $Phi_mu$ defined on a uniformly convex Banach space, and depending on a real parameter $mu$. More precisely, we show the existence of a sequence $(mu_n)$ such that $Phi_{mu_n}$ has a pair of critical points $pm u_n$ satisfying $Phi_{mu_n}(pm u_n)=0$, for every $n$. In addition, we provide some properties of $mu_n$ and $u_n$. This result, which is proved via a fibering map approach (based on the {it nonlinear generalized Rayleigh quotient} method cite{I1}) combined with the Ljusternik-Schnirelman theory, is then applied to several classes of elliptic pdes.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the existence of cylindrically symmetric traveling fronts of fractional Allen-Cahn equation in $mathbb{R}^{3}$ $mathbb{R}^{3}$中分数阶Allen-Cahn方程圆柱对称行前的存在性
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-09-01 DOI: 10.57262/die034-0910-467
Lü-Yi Ma, Zhi-Cheng Wang
{"title":"On the existence of cylindrically symmetric traveling fronts of fractional Allen-Cahn equation in $mathbb{R}^{3}$","authors":"Lü-Yi Ma, Zhi-Cheng Wang","doi":"10.57262/die034-0910-467","DOIUrl":"https://doi.org/10.57262/die034-0910-467","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41954518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Existence under lack of convexity 无凸性下的存在
IF 1.4 4区 数学
Differential and Integral Equations Pub Date : 2021-09-01 DOI: 10.57262/die034-0910-491
P. Pedregal
{"title":"Existence under lack of convexity","authors":"P. Pedregal","doi":"10.57262/die034-0910-491","DOIUrl":"https://doi.org/10.57262/die034-0910-491","url":null,"abstract":"","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46282328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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