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Ground state of the Gross–Pitaevskii equation with a harmonic potential in the energy-critical case 能量临界情况下具有谐波势的格罗斯-皮塔耶夫斯基方程的基态
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-02-28 DOI: 10.3233/asy-241897
Dmitry E. Pelinovsky, Szymon Sobieszek
{"title":"Ground state of the Gross–Pitaevskii equation with a harmonic potential in the energy-critical case","authors":"Dmitry E. Pelinovsky, Szymon Sobieszek","doi":"10.3233/asy-241897","DOIUrl":"https://doi.org/10.3233/asy-241897","url":null,"abstract":"Ground state of the energy-critical Gross–Pitaevskii equation with a harmonic potential can be constructed variationally. It exists in a finite interval of the eigenvalue parameter. The supremum norm of the ground state vanishes at one end of this interval and diverges to infinity at the other end.We explore the shooting method in the limit of large norm to prove that the ground state is pointwise close to the Aubin–Talenti solution of the energy-critical wave equation in near field and to the confluent hypergeometric function in far field. The shooting method gives the precise dependence of the eigenvalue parameter versus the supremum norm.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140317049","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
Dimension reduction and homogenization of composite plate with matrix pre-strain 带基体预应变的复合板尺寸减小和均质化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-02-19 DOI: 10.3233/asy-241896
Amartya Chakrabortty, Georges Griso, Julia Orlik
{"title":"Dimension reduction and homogenization of composite plate with matrix pre-strain","authors":"Amartya Chakrabortty, Georges Griso, Julia Orlik","doi":"10.3233/asy-241896","DOIUrl":"https://doi.org/10.3233/asy-241896","url":null,"abstract":"This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic perforated plate made of stiff material with holes filledby a soft matrix material. The structure is clamped on a cylindrical part. Two cases of asymptotic analysis are considered: one without pre-strain and the other with matrix pre-strain. In both cases, the total elastic energy is in the von-Kármán (vK) regime (ε5). A new splitting of the displacements is introduced to analyze the asymptotic behavior. The displacements are decomposed using the Kirchhoff–Love (KL) plate displacement decomposition. The use of a re-scaling unfolding operator allows for deriving the asymptotic behavior of the Green St. Venant’s strain tensor in terms of displacements. The limit homogenized energy is shown to be of vK type with linear elastic cell problems, established using the Γ-convergence. Additionally, it is shown that for isotropic homogenized material, our limit vK plate is orthotropic. The derived results have practical applications in the design and analysis of composite structures.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311000","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
Approximation diffusion for the Nonlinear Schrödinger equation with a random potential 具有随机势的非线性薛定谔方程的近似扩散
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-01-29 DOI: 10.3233/asy-241894
Grégoire Barrué, Arnaud Debussche, Maxime Tusseau
{"title":"Approximation diffusion for the Nonlinear Schrödinger equation with a random potential","authors":"Grégoire Barrué, Arnaud Debussche, Maxime Tusseau","doi":"10.3233/asy-241894","DOIUrl":"https://doi.org/10.3233/asy-241894","url":null,"abstract":"We prove that the stochastic Nonlinear Schrödinger (NLS) equation is the limit of NLS equation with random potential with vanishing correlation length. We generalize the perturbed test function method to the context of dispersive equations. Apart from the difficulty of working in infinite dimension, we treat the case of random perturbations which are not assumed uniformly bounded.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758144","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
Bound states of weakly deformed soft waveguides 弱变形软波导的边界态
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-01-24 DOI: 10.3233/asy-241893
Pavel Exner, Sylwia Kondej, Vladimir Lotoreichik
{"title":"Bound states of weakly deformed soft waveguides","authors":"Pavel Exner, Sylwia Kondej, Vladimir Lotoreichik","doi":"10.3233/asy-241893","DOIUrl":"https://doi.org/10.3233/asy-241893","url":null,"abstract":"In this paper we consider the two-dimensional Schrödinger operator with an attractive potential which is a multiple of the characteristic function of an unbounded strip-shaped region, whose thickness is varying and is determined by the function R∋x↦d+εf(x), where d>0 is a constant, ε>0 is a small parameter, and f is a compactly supported continuous function. We prove that if ∫Rfdx>0, then the respective Schrödinger operator has a unique simple eigenvalue below the threshold of the essential spectrum for all sufficiently small ε>0 and we obtain the asymptotic expansion of this eigenvalue in the regime ε→0. An asymptotic expansion of the respective eigenfunction as ε→0 is also obtained. In the case that ∫Rfdx<0 we prove that the discrete spectrum is empty for all sufficiently small ε>0. In the critical case ∫Rfdx=0, we derive a sufficient condition for the existence of a unique bound state for all sufficiently small ε>0.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139665273","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
New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type 从具有无限记忆和可变指数型非线性阻尼的第二频率谱看季莫申科系统的新衰减结果
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-01-24 DOI: 10.3233/asy-231892
A. Al‐Mahdi
{"title":"New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type","authors":"A. Al‐Mahdi","doi":"10.3233/asy-231892","DOIUrl":"https://doi.org/10.3233/asy-231892","url":null,"abstract":"In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related results in the literature.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601952","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 a biharmonic coupled system with non-standard nonlinearity: Existence, blow up and numerics 关于具有非标准非线性的双谐波耦合系统：存在、爆炸和数值
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-01-16 DOI: 10.3233/asy-231891
O. Bouhoufani, S. Messaoudi, M. Alahyane
{"title":"On a biharmonic coupled system with non-standard nonlinearity: Existence, blow up and numerics","authors":"O. Bouhoufani, S. Messaoudi, M. Alahyane","doi":"10.3233/asy-231891","DOIUrl":"https://doi.org/10.3233/asy-231891","url":null,"abstract":"In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To illustrate our theoritical findings, we present two numerical examples.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139618235","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
Recovery of a general nonlinearity in the semilinear wave equation 半线性波方程中一般非线性的恢复
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-01-02 DOI: 10.3233/asy-231890
Antônio Sá Barreto, Plamen Stefanov
{"title":"Recovery of a general nonlinearity in the semilinear wave equation","authors":"Antônio Sá Barreto, Plamen Stefanov","doi":"10.3233/asy-231890","DOIUrl":"https://doi.org/10.3233/asy-231890","url":null,"abstract":"We study the inverse problem of recovery a nonlinearity f(t,x,u), which is compactly supported in x, in the semilinear wave equation utt−Δu+f(t,x,u)=0. We probe the medium with either complex or real-valued harmonic waves of wavelength ∼h and amplitude ∼1. They propagate in a regime where the nonlinearity affects the subprincipal but not the principal term, except for the zeroth harmonics. We measure the transmitted wave when it exits suppxf. We show that one can recover f(t,x,u) when it is an odd function of u, and we can recover α(x) when f(t,x,u)=α(x)u2m. This is done in an explicit way as h→0.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139664972","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 and regularity of solutions of nonlinear anisotropic elliptic problem with Hardy potential 带哈迪势的非线性各向异性椭圆问题解的存在性和正则性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-12-22 DOI: 10.3233/asy-231889
H. Khelifi
{"title":"Existence and regularity of solutions of nonlinear anisotropic elliptic problem with Hardy potential","authors":"H. Khelifi","doi":"10.3233/asy-231889","DOIUrl":"https://doi.org/10.3233/asy-231889","url":null,"abstract":"In this paper, we are interested in the existence and regularity of solutions for some anisotropic elliptic equations with Hardy potential and L m ( Ω ) data in appropriate anisotropic Sobolev spaces. The aim of this work is to get natural conditions to show the existence and regularity results for the solutions, that is related to an anisotropic Hardy inequality.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138945670","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
Polynomial stability of thermoelastic Timoshenko system with non-global time-delayed Cattaneo’s law 具有非全局延时卡塔尼奥定律的热弹性季莫申科系统的多项式稳定性
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-12-21 DOI: 10.3233/asy-231888
Haidar Badawi, Hawraa Alsayed
{"title":"Polynomial stability of thermoelastic Timoshenko system with non-global time-delayed Cattaneo’s law","authors":"Haidar Badawi, Hawraa Alsayed","doi":"10.3233/asy-231888","DOIUrl":"https://doi.org/10.3233/asy-231888","url":null,"abstract":"In this paper, we consider a one dimensional thermoelastic Timoshenko system in which the heat flux is given by Cattaneo’s law and acts locally on the bending moment with a time delay. We prove its well-posedness, strong stability, and polynomial stability.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139083547","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
Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces 时间相关空间上具有记忆的非经典扩散方程的长时行为
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2023-12-12 DOI: 10.3233/asy-231887
Jiangwei Zhang, Zhe Xie, Yongqin Xie
{"title":"Long-time behavior of nonclassical diffusion equations with memory on time-dependent spaces","authors":"Jiangwei Zhang, Zhe Xie, Yongqin Xie","doi":"10.3233/asy-231887","DOIUrl":"https://doi.org/10.3233/asy-231887","url":null,"abstract":"This paper aims to study the long-time behavior of nonclassical diffusion equation with memory and disturbance parameters on time-dependent space. By using the contractive process method on the family of time-dependent spaces and operator decomposition technique, the existence of pullback attractors is first proved. Then the upper semi-continuity of pullback attractors with respect to perturbation parameter ν in M t is obtained. It’s remarkable that the nonlinearity f satisfies the polynomial growth of arbitrary order.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009137","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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