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Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction 圆柱域中在一个方向上变得无界的非线性椭圆特征值问题
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-04-23 DOI: 10.3233/asy-241907
Rama Rawat, Haripada Roy, Prosenjit Roy
{"title":"Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction","authors":"Rama Rawat, Haripada Roy, Prosenjit Roy","doi":"10.3233/asy-241907","DOIUrl":"https://doi.org/10.3233/asy-241907","url":null,"abstract":"The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the cylindrical domains tends to infinity. This generalises an earlier work of Chipot et al. (Asymptot. Anal. 85(3–4) (2013) 199–227) where the linear case p=2 is studied. Asymptotic behavior of all the higher eigenvalues of the linear case and the second eigenvalues of general case (using topological degree) for such problems is also studied.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519164","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
Asymptotic behaviour of some anisotropic problems 一些各向异性问题的渐近行为
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-04-23 DOI: 10.3233/asy-241906
Michel Chipot
{"title":"Asymptotic behaviour of some anisotropic problems","authors":"Michel Chipot","doi":"10.3233/asy-241906","DOIUrl":"https://doi.org/10.3233/asy-241906","url":null,"abstract":"The goal of this paper is to explore the asymptotic behaviour of anisotropic problems governed by operators of the pseudo p-Laplacian type when the size of the domain goes to infinity in different directions.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140669113","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
An optimal control problem for diffusion–precipitation model1 扩散沉淀模型的优化控制问题1
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-04-23 DOI: 10.3233/asy-241905
A. Kundu, H. S. Mahato
{"title":"An optimal control problem for diffusion–precipitation model1","authors":"A. Kundu, H. S. Mahato","doi":"10.3233/asy-241905","DOIUrl":"https://doi.org/10.3233/asy-241905","url":null,"abstract":"We present an optimal control problem associated to a chemical transportation phenomena in a periodic porous medium. Posing controls on the porous part of the medium (distributed control), we set up a convex minimization problem. The main objective of this article is to characterize an arbitrary control to be an optimal control. We establish a relation between the optimal control and the corresponding adjoint state. At first, we analyse the microscopic description of the controlled system, then we homogenised the system by rigorous two-scale convergence method and periodic unfolding method.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140670868","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
Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity 具有一般非线性的准线性薛定谔方程的归一化解
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-04-16 DOI: 10.3233/asy-241908
Ting Deng, Marco Squassina, Jianjun Zhang, Xuexiu Zhong
{"title":"Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity","authors":"Ting Deng, Marco Squassina, Jianjun Zhang, Xuexiu Zhong","doi":"10.3233/asy-241908","DOIUrl":"https://doi.org/10.3233/asy-241908","url":null,"abstract":"We are concerned with solutions of the following quasilinear Schrödinger equations −div(φ2(u)∇u)+φ(u)φ′(u)|∇u|2+λu=f(u),x∈RN with prescribed mass ∫RNu2dx=c, where N⩾3, c>0, λ∈R appears as the Lagrange multiplier and φ∈C1(R,R+). The nonlinearity f∈C(R,R) is allowed to be mass-subcritical, mass-critical and mass-supercritical at origin and infinity. Via a dual approach, the fixed point index and a global branch approach, we establish the existence of normalized solutions to the problem above. The results extend previous results by L. Jeanjean, J. J. Zhang and X.X. Zhong to the quasilinear case.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508378","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 Boussinesq system with fractional memory in pseudo-measure spaces 关于伪测量空间中具有分数记忆的布森斯克系统
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-25 DOI: 10.3233/asy-241904
Felipe Poblete, Clessius Silva, A. Viana
{"title":"On the Boussinesq system with fractional memory in pseudo-measure spaces","authors":"Felipe Poblete, Clessius Silva, A. Viana","doi":"10.3233/asy-241904","DOIUrl":"https://doi.org/10.3233/asy-241904","url":null,"abstract":"This paper studies the existence of local and global self-similar solutions for a Boussinesq system with fractional memory and fractional diffusions u t + u · ∇ u + ∇ p + ν ( − Δ ) β u = θ f , x ∈ R n , t > 0 , θ t + u · ∇ θ + g α ∗ ( − Δ ) γ θ = 0 , x ∈ R n , t > 0 , div u = 0 , x ∈ R n , t > 0 , u ( x , 0 ) = u 0 , θ ( x , 0 ) = θ 0 , x ∈ R n , where g α ( t ) = t α − 1 Γ ( α ) . The existence results are obtained in the framework of pseudo-measure spaces. We find that the existence and self-similarity of global solutions is strongly influenced by the relationship among the memory and the fractional diffusions. Indeed, we obtain the existence and self-similarity of global solutions only when γ = ( α + 1 ) β. Moreover, we prove a stability result for the global solutions and the existence of asymptotically self-similar solutions.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140381384","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
Non-trivial solutions for the fractional Schrödinger–Poisson system with p-Laplacian 带 p 拉普拉卡方的分数薛定谔-泊松系统的非微观解
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-25 DOI: 10.3233/asy-241903
Chungen Liu, Yuyou Zhong, Jiabin Zuo
{"title":"Non-trivial solutions for the fractional Schrödinger–Poisson system with p-Laplacian","authors":"Chungen Liu, Yuyou Zhong, Jiabin Zuo","doi":"10.3233/asy-241903","DOIUrl":"https://doi.org/10.3233/asy-241903","url":null,"abstract":"In this paper, we study a fractional Schrödinger–Poisson system with p-Laplacian. By using some scaling transformation and cut-off technique, the boundedness of the Palais–Smale sequences at the mountain pass level is gotten. As a result, the existence of non-trivial solutions for the system is obtained.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140381714","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
Effective medium theory for second-gradient elasticity with chirality 具有手性的第二梯度弹性的有效介质理论
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-12 DOI: 10.3233/asy-241902
Grigor Nika, Adrian Muntean
{"title":"Effective medium theory for second-gradient elasticity with chirality","authors":"Grigor Nika, Adrian Muntean","doi":"10.3233/asy-241902","DOIUrl":"https://doi.org/10.3233/asy-241902","url":null,"abstract":"We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities ℓ, the intrinsic lengths of the constituents ℓSG and ℓchiral, and the overall characteristic length of the domain L. Depending on the different scale interactions between ℓSG, ℓchiral, ℓ, and L we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors’ structure rely on a suitable use of the periodic unfolding operator.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140802820","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
Optimal convergence rate for homogenization of convex Hamilton–Jacobi equations in the periodic spatial-temporal environment 周期性时空环境中凸汉密尔顿-雅可比方程均质化的最佳收敛速率
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-12 DOI: 10.3233/asy-241898
Hoang Nguyen-Tien
{"title":"Optimal convergence rate for homogenization of convex Hamilton–Jacobi equations in the periodic spatial-temporal environment","authors":"Hoang Nguyen-Tien","doi":"10.3233/asy-241898","DOIUrl":"https://doi.org/10.3233/asy-241898","url":null,"abstract":"We study the optimal convergence rate for the homogenization problem of convex Hamilton–Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that of (Tran and Yu (2021)), which means the optimal convergence rate is also O(ε).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140802628","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
Decay characterization of solutions to incompressible Navier–Stokes–Voigt equations 不可压缩 Navier-Stokes-Voigt 方程解的衰减特征
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-07 DOI: 10.3233/asy-241900
Jitao Liu, Shasha Wang, Wen-Qing Xu
{"title":"Decay characterization of solutions to incompressible Navier–Stokes–Voigt equations","authors":"Jitao Liu, Shasha Wang, Wen-Qing Xu","doi":"10.3233/asy-241900","DOIUrl":"https://doi.org/10.3233/asy-241900","url":null,"abstract":"Recently, Niche [J. Differential Equations, 260 (2016), 4440–4453] established upper bounds on the decay rates of solutions to the 3D incompressible Navier–Stokes–Voigt equations in terms of the decay character r∗ of the initial data in H1(R3). Motivated by this work, we focus on characterizing thelarge-time behavior of all space-time derivatives of the solutions for the 2D case and establish upper bounds and lower bounds on their decay rates by making use of the decay character and Fourier splitting methods. In particular, for the case −n2<r∗⩽1, we verify the optimality of the upper bounds, which is new to the best of our knowledge. Similar improved decay results are also true for the 3D case.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140314983","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
Global well-posedness and L 2 decay estimate of smooth solutions for the 3-D incompressible Navier–Stokes–Allen–Cahn system 三维不可压缩纳维-斯托克斯-阿伦-卡恩系统平稳解的全局好求和 L 2 衰减估计
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-03-07 DOI: 10.3233/asy-241901
Wenwen Huo, Kaimin Teng, Chao Zhang
{"title":"Global well-posedness and L 2 decay estimate of smooth solutions for the 3-D incompressible Navier–Stokes–Allen–Cahn system","authors":"Wenwen Huo, Kaimin Teng, Chao Zhang","doi":"10.3233/asy-241901","DOIUrl":"https://doi.org/10.3233/asy-241901","url":null,"abstract":"We consider the Cauchy problem for the 3-D incompressible Navier–Stokes–Allen–Cahn system, which can effectively describe large deformations or topological deformations. Under the assumptions of small initial data, we study the global well-posedness and time-decay of solutions to such system by means of pure energy method and Fourier-splitting technique.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140077354","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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