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A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional 关于Ambrosio–Tortorelli泛函一维临界点的一个注记
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-08-29 DOI: 10.3233/asy-231857
Jean-François Babadjian, V. Millot, Rémy Rodiac
{"title":"A note on the one-dimensional critical points of the Ambrosio–Tortorelli functional","authors":"Jean-François Babadjian, V. Millot, Rémy Rodiac","doi":"10.3233/asy-231857","DOIUrl":"https://doi.org/10.3233/asy-231857","url":null,"abstract":"This note addresses the question of convergence of critical points of the Ambrosio–Tortorelli functional in the one-dimensional case under pure Dirichlet boundary conditions. An asymptotic analysis argument shows the convergence to two possible limits points: either a globally affine function or a step function with a single jump at the middle point of the space interval, which are both critical points of the one-dimensional Mumford–Shah functional under a Dirichlet boundary condition. As a byproduct, non minimizing critical points of the Ambrosio–Tortorelli functional satisfying the energy convergence assumption as in (Babadjian, Millot and Rodiac (2022)) are proved to exist.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48831720","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
Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs 基于Liouville型结果和其他极大值原理的完备超曲面的刚度和不存在性及其在全图中的应用
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-08-23 DOI: 10.3233/asy-231858
Railane Antonia, Giovanni Molica Bisci, Henrique F. de Lima, Márcio S. Santos
{"title":"Rigidity and nonexistence of complete hypersurfaces via Liouville type results and other maximum principles, with applications to entire graphs","authors":"Railane Antonia, Giovanni Molica Bisci, Henrique F. de Lima, Márcio S. Santos","doi":"10.3233/asy-231858","DOIUrl":"https://doi.org/10.3233/asy-231858","url":null,"abstract":"We investigate complete hypersurfaces with some positive higher order mean curvature in a semi-Riemannian warped product space. Under standard curvature conditions on the ambient space and appropriate constraints on the higher order mean curvatures, we establish rigidity and nonexistence results via Liouville type results and suitable maximum principles related to the divergence of smooth vector fields on a complete noncompact Riemannian manifold. Applications to standard warped product models, like the Schwarzschild, Reissner-Nordström and pseudo-hyperbolic spaces, as well as steady state type spacetimes, are given and a particular study of entire graphs is also presented.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46371180","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
Stabilization for the Klein–Gordon–Zakharov system Klein-Gordon-Zakharov系统的稳定
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-08-18 DOI: 10.3233/asy-231856
Weijia Li, Yuqi Shangguan, Weiping Yan
{"title":"Stabilization for the Klein–Gordon–Zakharov system","authors":"Weijia Li, Yuqi Shangguan, Weiping Yan","doi":"10.3233/asy-231856","DOIUrl":"https://doi.org/10.3233/asy-231856","url":null,"abstract":"This paper deals with global stability dynamics for the Klein–Gordon–Zakharov system in R 2 . We first establish that this system admits a family of linear mode unstable explicit quasi-periodic wave solutions. Next, we prove that the Kelvin–Voigt damping can help to stabilize those linear mode unstable explicit quasi-periodic wave solutions for the Klein–Gordon–Zakharov system in the Sobolev space H s + 1 ( R 2 ) × H s + 1 ( R 2 ) × H s + 1 ( R 2 ) for any s ⩾ 1. Moreover, the Kelvin–Voigt damped Klein–Gordon–Zakharov system admits a unique Sobolev regular solution exponentially convergent to some special solutions (including quasi-periodic wave solutions) of it. Our result can be extended to the n-dimension dissipative Klein–Gordon–Zakharov system for any n ⩾ 1.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43480472","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
Semilinear hyperbolic inequalities with Hardy potential in a bounded domain 有界域中具有Hardy势的半线性双曲不等式
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-08-11 DOI: 10.3233/asy-231854
M. Jleli, B. Samet
{"title":"Semilinear hyperbolic inequalities with Hardy potential in a bounded domain","authors":"M. Jleli, B. Samet","doi":"10.3233/asy-231854","DOIUrl":"https://doi.org/10.3233/asy-231854","url":null,"abstract":"We consider hyperbolic inequalities with Hardy potential u t t − Δ u + λ | x | 2 u ⩾ | x | − a | u | p in  ( 0 , ∞ ) × B 1 ∖ { 0 } , u ( t , x ) ⩾ f ( x ) on  ( 0 , ∞ ) × ∂ B 1 , where B 1 is the unit ball in R N , N ⩾ 3, λ > − ( N − 2 2 ) 2 , a ⩾ 0, p > 1 and f is a nontrivial L 1 -function. We study separately the cases: λ = 0, − ( N − 2 2 ) 2 < λ < 0 and λ > 0. For each case, we obtain an optimal criterium for the nonexistence of weak solutions. Our study yields naturally optimal nonexistence results for the corresponding stationary problem. The novelty of this work lies in two facts: (i) To the best of our knowledge, in all previous works dealing with nonexistence results for evolution equations with Hardy potential in a bounded domain, only the parabolic case has been investigated, making use of some comparison principles. (ii) To the best of our knowledge, in all previous works, the issue of nonexistence has been studied only in the case of positive solutions. In this paper, there is no restriction on the sign of solutions.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49345373","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
Topological sensitivity analysis for the 3D nonlinear Navier–Stokes equations 三维非线性Navier-Stokes方程的拓扑灵敏度分析
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-08-11 DOI: 10.3233/asy-231855
M. Hassine, M. Ouni
{"title":"Topological sensitivity analysis for the 3D nonlinear Navier–Stokes equations","authors":"M. Hassine, M. Ouni","doi":"10.3233/asy-231855","DOIUrl":"https://doi.org/10.3233/asy-231855","url":null,"abstract":"This work is devoted to a topological asymptotic expansion for the nonlinear Navier–Stokes operator. We consider the 3D Navier–Stokes equations as a model problem and we derive a topological sensitivity analysis for a design function with respect to the insertion of a small obstacle inside the fluid flow domain. The asymptotic behavior of the perturbed velocity field with respect to the obstacle size is examined. The performed mathematical framework can be applied for a large class of design functions and arbitrarily shaped geometric perturbations. The obtained asymptotic formula can serve as a useful tool for solving a variety of topology optimization problems in fluid mechanics.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46908542","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
Concavity principles for nonautonomous elliptic equations and applications 非自治椭圆方程的凹性原理及其应用
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-07-11 DOI: 10.3233/asy-231863
N. Almousa, Claudia Bucur, Roberta Cornale, M. Squassina
{"title":"Concavity principles for nonautonomous elliptic equations and applications","authors":"N. Almousa, Claudia Bucur, Roberta Cornale, M. Squassina","doi":"10.3233/asy-231863","DOIUrl":"https://doi.org/10.3233/asy-231863","url":null,"abstract":"In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45446365","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 semi-classical analysis of Schrödinger operators with linear electric potentials on a bounded domain 关于有界域上具有线性电势的Schrödinger算子的半经典分析
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-06-30 DOI: 10.3233/asy-231848
Rayan Fahs
{"title":"On the semi-classical analysis of Schrödinger operators with linear electric potentials on a bounded domain","authors":"Rayan Fahs","doi":"10.3233/asy-231848","DOIUrl":"https://doi.org/10.3233/asy-231848","url":null,"abstract":"The aim of this paper is to establish the asymptotic expansion of the eigenvalues of the Stark Hamiltonian, with a strong uniform electric field and Dirichlet boundary conditions on a smooth bounded domain of R N , N ⩾ 2. This work aims at generalizing the recent results of Cornean, Krejčiřik, Pedersen, Raymond, and Stockmeyer in dimension 2. More precisely, in dimension N, in the strong electric field limit, we derive, under certain local convexity conditions, a full asymptotic expansion of the low-lying eigenvalues. To establish our main result, we perform the construction of quasi-modes. The “optimality” of our constructions is then established thanks to a reduction to model operators and localization estimates.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45871466","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
Arched beams of Bresse type: New thermal couplings and pattern of stability Bresse型拱形梁：新型热耦合和稳定性模式
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-06-30 DOI: 10.3233/asy-231850
G.E. Bittencourt Moraes, S.J. de Camargo, M.A. Jorge Silva
{"title":"Arched beams of Bresse type: New thermal couplings and pattern of stability","authors":"G.E. Bittencourt Moraes, S.J. de Camargo, M.A. Jorge Silva","doi":"10.3233/asy-231850","DOIUrl":"https://doi.org/10.3233/asy-231850","url":null,"abstract":"This is the second paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under Fourier’s law. Differently of the first one, where the thermal couplings are regarded on the axial and bending displacements, here the thermal couplings are taken over the shear and bending forces. Such thermal effects still result in a new prototype of partially damped Bresse system whose stability results demand a proper approach. Combining a novel path of local estimates by means of the resolvent equation along with a control-observability analysis developed for elastic non-homogeneous systems of Bresse type proposed in trilogy’s first paper, we are able to provide a unified methodology of the asymptotic stability results, by proving the pattern of them with respect to boundary conditions and the action of temperature couplings, which is in compliance with our previous and present goal.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48031232","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 asymptotic behavior of the energy for evolution models with oscillating time-dependent damping 振荡含时阻尼演化模型能量的渐近性态
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-06-30 DOI: 10.3233/asy-231851
Halit Sevki Aslan, Marcelo Rempel Ebert
{"title":"On the asymptotic behavior of the energy for evolution models with oscillating time-dependent damping","authors":"Halit Sevki Aslan, Marcelo Rempel Ebert","doi":"10.3233/asy-231851","DOIUrl":"https://doi.org/10.3233/asy-231851","url":null,"abstract":"In the present paper, we study the influence of oscillations of the time-dependent damping term b ( t ) u t on the asymptotic behavior of the energy for solutions to the Cauchy problem for a σ-evolution equation u t t + ( − Δ ) σ u + b ( t ) u t = 0 , ( t , x ) ∈ [ 0 , ∞ ) × R n , u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) , x ∈ R n , where σ > 0 and b is a continuous and positive function. Mainly we consider damping terms that are perturbations of the scale invariant case b ( t ) = β ( 1 + t ) − 1 , with β > 0, and we discuss the influence of oscillations of b on the energy estimates according to the size of β.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46884889","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
Bifurcation and stability for charged drops 带电液滴的分岔与稳定性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-06-29 DOI: 10.3233/asy-231853
Guowei Dai, Ben Duan, Fang Liu
{"title":"Bifurcation and stability for charged drops","authors":"Guowei Dai, Ben Duan, Fang Liu","doi":"10.3233/asy-231853","DOIUrl":"https://doi.org/10.3233/asy-231853","url":null,"abstract":"In this paper, we investigate the Laplace’s equation for the electrical potential of charge drops on exterior domain, and overdetermined boundary conditions are prescribed. We determine the local bifurcation structure with respect to the surface tension coefficient as bifurcation parameter. Furthermore, we establish the stability and the instability near the bifurcation point.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42607144","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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