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Homogenization of elliptic PDE with L 1 source term in domains with boundary having very general oscillations 源项为L的椭圆偏微分方程在边界具有非常一般振荡域上的均匀化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-10-05 DOI: 10.3233/asy-221808
A. K. Nandakumaran, A. Sufian, Renjith Thazhathethil
{"title":"Homogenization of elliptic PDE with L 1 source term in domains with boundary having very general oscillations","authors":"A. K. Nandakumaran, A. Sufian, Renjith Thazhathethil","doi":"10.3233/asy-221808","DOIUrl":"https://doi.org/10.3233/asy-221808","url":null,"abstract":"In the present article, we study the homogenization of a second-order elliptic PDE with oscillating coefficients in two different domains, namely a standard rectangular domain with very general oscillations and a circular type oscillating domain. Further, we consider the source term in L 1 and hence the solutions are interpreted as renormalized solutions. In the first domain, oscillations are in horizontal directions, while that of the second one is in the angular direction. To take into account the type of oscillations, we have used two different types of unfolding operators and have studied the asymptotic behavior of the renormalized solution of a second-order linear elliptic PDE with a source term in L 1 . In fact, we begin our study in oscillatory circular domain with oscillating coefficients and L 2 data which is also new in the literature. We also prove relevant strong convergence (corrector) results. We present the complete details in the context of circular domains, and sketch the proof in other domain.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45903720","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
A perturbed fractional p-Kirchhoff problem with critical nonlinearity 具有临界非线性的摄动分数阶p-Kirchhoff问题
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-10-03 DOI: 10.3233/asy-221809
Luigi Appolloni, A. Fiscella, S. Secchi
{"title":"A perturbed fractional p-Kirchhoff problem with critical nonlinearity","authors":"Luigi Appolloni, A. Fiscella, S. Secchi","doi":"10.3233/asy-221809","DOIUrl":"https://doi.org/10.3233/asy-221809","url":null,"abstract":"We consider a quasilinear partial differential equation governed by the p-Kirchhoff fractional operator. By using variational methods, we prove several results concerning the existence of solutions and their stability properties with respect to some parameters.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44066865","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
Topological asymptotic expansion for the full Navier–Stokes equations 全Navier-Stokes方程的拓扑渐近展开
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-30 DOI: 10.3233/asy-221807
M. Hassine, Sana Chaouch
{"title":"Topological asymptotic expansion for the full Navier–Stokes equations","authors":"M. Hassine, Sana Chaouch","doi":"10.3233/asy-221807","DOIUrl":"https://doi.org/10.3233/asy-221807","url":null,"abstract":"This paper is concerned with a topological sensitivity analysis for the two dimensional incompressible Navier–Stokes equations. We derive a topological asymptotic expansion for a shape functional with respect to the creation of a small geometric perturbation inside the fluid flow domain. The geometric perturbation is modeled as a small obstacle. The asymptotic behavior of the perturbed velocity field with respect to the obstacle size is discussed. The obtained results are valid for a large class of shape fonctions and arbitrarily shaped geometric perturbations. The established topological asymptotic expansion provides a useful tool for shape and topology optimization in fluid mechanics.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45544525","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
Semi-classical states for the Choquard equations with doubly critical exponents: Existence, multiplicity and concentration 双临界指数Choquard方程的半经典状态:存在性、多重性和集中性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-13 DOI: 10.3233/asy-221799
Yujian Su, Zhisu Liu
{"title":"Semi-classical states for the Choquard equations with doubly critical exponents: Existence, multiplicity and concentration","authors":"Yujian Su, Zhisu Liu","doi":"10.3233/asy-221799","DOIUrl":"https://doi.org/10.3233/asy-221799","url":null,"abstract":"In this paper, we are concerned with a class of Choquard equation with the lower and upper critical exponents in the sense of the Hardy–Littlewood–Sobolev inequality. We emphasize that nonlinearities with doubly critical exponents are totally different from the well-known Berestycki–Lions-type ones. Working in a variational setting, we prove the existence, multiplicity and concentration of positive solutions for such equations when the potential satisfies some suitable conditions. We show that the number of positive solutions depends on the profile of the potential and that each solution concentrates around its corresponding global minimum point of the potential in the semi-classical limit.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43952964","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 a Cahn–Hilliard–Oono model for image segmentation 关于图像分割的Cahn–Hilliard–Oono模型
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-12 DOI: 10.3233/asy-221801
Lu Li
{"title":"On a Cahn–Hilliard–Oono model for image segmentation","authors":"Lu Li","doi":"10.3233/asy-221801","DOIUrl":"https://doi.org/10.3233/asy-221801","url":null,"abstract":"This paper studies firstly the well-posedness and the asymptotic behavior of a Cahn–Hilliard–Oono type model, with cubic nonlinear terms, which is proposed for image segmentation. In particular, the existences of the global attractor and the exponential attractor have been proved, and it shows that the fractal dimension of the global attractor will tend to infinity as α → 0. The difficulty here is that we no longer have the conservation of mass. Furthermore, this model with logarithmic nonlinear terms has been studied as well. One difficulty here is to make sure that the logarithmic terms can pass to the limit under the standard Galerkin scheme. Another difficulty is to prove additional regularities on the solutions which is essential to prove a strict separation from the pure states 0 and 1 in one and two space dimensions. It eventually shows that the dimension of the global attractor is finite by proving the existence of the exponential attractor.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45158176","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
Stability analysis of laminated beams with Kelvin–Voigt damping and strong time delay Kelvin–Voigt阻尼和强时滞叠层梁的稳定性分析
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-12 DOI: 10.3233/asy-221802
C. Nonato, C. Raposo, B. Feng, A. Ramos
{"title":"Stability analysis of laminated beams with Kelvin–Voigt damping and strong time delay","authors":"C. Nonato, C. Raposo, B. Feng, A. Ramos","doi":"10.3233/asy-221802","DOIUrl":"https://doi.org/10.3233/asy-221802","url":null,"abstract":"In this paper we consider a model of laminated beams combining viscoelastic damping and strong time-delayed damping. The global well-posedness is proved by using the theory of semigroups of linear operators. We prove the lack of exponential stability when the speed wave propagations are not equal. In fact, we show in this situation, that the system goes to zero polynomially with rate t − 1 / 2 . On the other hand, by constructing some suitable multipliers, we establish that the energy decays exponentially provided the equal-speed wave propagations hold.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47585851","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
Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method 具有动态间隙连接的心脏电活动的微观三域模型。第二部分-用展开均匀化方法推导宏观三域模型
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-08 DOI: 10.3233/ASY-221804
Fakhrielddine Bader, M. Bendahmane, Mazen Saad, Raafat Talhouk
{"title":"Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 – Derivation of the macroscopic tridomain model by unfolding homogenization method","authors":"Fakhrielddine Bader, M. Bendahmane, Mazen Saad, Raafat Talhouk","doi":"10.3233/ASY-221804","DOIUrl":"https://doi.org/10.3233/ASY-221804","url":null,"abstract":"We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1–35), we detail this model in which gap junctions are considered as the connections between adjacent cells in cardiac muscle and could serve as alternative or supporting pathways for cell-to-cell electrical signal propagation. Departing from this microscopic cellular model, we apply the periodic unfolding method to derive the macroscopic tridomain model. Several difficulties prevent the application of unfolding homogenization results, including the degenerate temporal structure of the tridomain equations and a nonlinear dynamic boundary condition on the cellular membrane. To prove the convergence of the nonlinear terms, especially those defined on the microscopic interface, we use the boundary unfolding operator and a Kolmogorov–Riesz compactness’s result.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49276814","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
Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion 具有异常扩散的非自治反应扩散方程的动力学和正则性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-07 DOI: 10.3233/asy-221800
Xingjie Yan, Shubin Wang, Xinguang Yang, Junzhao Zhang
{"title":"Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion","authors":"Xingjie Yan, Shubin Wang, Xinguang Yang, Junzhao Zhang","doi":"10.3233/asy-221800","DOIUrl":"https://doi.org/10.3233/asy-221800","url":null,"abstract":"This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L 2 ( Ω ) and H 0 α ( Ω ) ( 0 < α < 1) have been achieved with a restriction on the growth order of nonlinearity as 2 ⩽ p ⩽ 2 ( n − α ) n − 2 α . The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48241273","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
A strong maximum principle for mixed local and nonlocal p-Laplace equations 混合局部和非局部p-Laplace方程的一个强极大值原理
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-09-07 DOI: 10.3233/asy-221803
Bin Shang, Chao Zhang
{"title":"A strong maximum principle for mixed local and nonlocal p-Laplace equations","authors":"Bin Shang, Chao Zhang","doi":"10.3233/asy-221803","DOIUrl":"https://doi.org/10.3233/asy-221803","url":null,"abstract":"We establish a strong maximum principle for weak solutions of the mixed local and nonlocal p-Laplace equation − Δ p u + ( − Δ ) p s u = c ( x ) | u | p − 2 u in  Ω , where Ω ⊂ R N is an open set, p ∈ ( 1 , ∞ ), s ∈ ( 0 , 1 ) and c ∈ C ( Ω ‾ ).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42354316","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
Collective motion driven by nutrient consumption 由营养消耗驱动的集体运动
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2022-08-31 DOI: 10.3233/asy-221820
P. Jabin, B. Perthame
{"title":"Collective motion driven by nutrient consumption","authors":"P. Jabin, B. Perthame","doi":"10.3233/asy-221820","DOIUrl":"https://doi.org/10.3233/asy-221820","url":null,"abstract":"A classical problem describing the collective motion of cells, is the movement driven by consumption/depletion of a nutrient. Here we analyze one of the simplest such model written as a coupled Partial Differential Equation/Ordinary Differential Equation system which we scale so as to get a limit describing the usually observed pattern. In this limit the cell density is concentrated as a moving Dirac mass and the nutrient undergoes a discontinuity. We first carry out the analysis without diffusion, getting a complete description of the unique limit. When diffusion is included, we prove several specific a priori estimates and interpret the system as a heterogeneous monostable equation. This allow us to obtain a limiting problem which shows the concentration effect of the limiting dynamics.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42609196","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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