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Asymptotic Analysis最新文献

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Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension 一维薛定谔算子共振的奇异性和渐近分布
IF 1.1 4区 数学
Asymptotic Analysis Pub Date : 2024-08-08 DOI: 10.3233/asy-241928
T. J. Christiansen, T. Cunningham
{"title":"Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension","authors":"T. J. Christiansen, T. Cunningham","doi":"10.3233/asy-241928","DOIUrl":"https://doi.org/10.3233/asy-241928","url":null,"abstract":"We obtain new results about the high-energy distribution of resonances for the one-dimensional Schrödinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients, refining methods used in (J. Differential Equations 137(2) (1997) 251–272) and (J. Funct. Anal. 178(2) (2000) 396–420).","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141926123","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
Approximate kink-kink solutions for the ϕ6 model in the low-speed limit ϕ6模型在低速极限下的近似扭结解
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-30 DOI: 10.3233/asy-241917
Abdon Moutinho
{"title":"Approximate kink-kink solutions for the ϕ6 model in the low-speed limit","authors":"Abdon Moutinho","doi":"10.3233/asy-241917","DOIUrl":"https://doi.org/10.3233/asy-241917","url":null,"abstract":"In this paper, we consider the problem of elasticity and stability of the collision of two kinks with low speed v for the nonlinear wave equation known as the ϕ6 model in dimension 1+1. We construct a sequence of approximate solutions (ϕk(v,t,x))k∈N⩾2 for this model to understand the effects of thecollision in the movement of each soliton during a large time interval. The construction uses a new asymptotic method which is not only restricted to the ϕ6 model.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198510","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
Cahn–Hilliard system with proliferation term 带增殖项的卡恩-希利亚德系统
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-29 DOI: 10.3233/asy-241915
Aymard Christbert Nimi, Franck Davhys Reval Langa
{"title":"Cahn–Hilliard system with proliferation term","authors":"Aymard Christbert Nimi, Franck Davhys Reval Langa","doi":"10.3233/asy-241915","DOIUrl":"https://doi.org/10.3233/asy-241915","url":null,"abstract":"In this article, our objective is to explore a Cahn–Hilliard system with a proliferation term, particularly relevant in biological contexts, with Neumann boundary conditions. We commence our investigation by establishing the boundedness of the average values of the local cell density u and the temperature H. This observation suggests that the solution (u,H) either persists globally in time or experiences finite-time blow-up. Subsequently, we prove the convergence of u to 1 and H to 0 as time approaches infinity. Finally, we bolster our theoretical findings with numerical simulations.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198667","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
Ground state solutions for the Hamilton–Choquard elliptic system with critical exponential growth 具有临界指数增长的汉密尔顿-邱卡椭圆系统的基态解
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-29 DOI: 10.3233/asy-241916
Minlan Guan, Lizhen Lai, Boxue Liu, Dongdong Qin
{"title":"Ground state solutions for the Hamilton–Choquard elliptic system with critical exponential growth","authors":"Minlan Guan, Lizhen Lai, Boxue Liu, Dongdong Qin","doi":"10.3233/asy-241916","DOIUrl":"https://doi.org/10.3233/asy-241916","url":null,"abstract":"In this paper, we study the following Hamilton–Choquard type elliptic system: −Δu+u=(Iα∗F(v))f(v),x∈R2,−Δv+v=(Iβ∗F(u))f(u),x∈R2, where Iα and Iβ are Riesz potentials, f:R→R possessing critical exponential growth at infinity and F(t)=∫0tf(s)ds. Without the classic Ambrosetti–Rabinowitz conditionand strictly monotonic condition on f, we will investigate the existence of ground state solution for the above system. The strongly indefinite characteristic of the system, combined with the convolution terms and critical exponential growth, makes such problem interesting and challenging to study. With the help of a proper auxiliary system, we employ an approximation scheme and the non-Nehari manifold method to control the minimax levels by a fine threshold, and succeed in restoring the compactness for the critical problem. Existence of a ground state solution is finally established by the concentration compactness argument and some detailed estimates.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198666","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 elliptic problem in dimension N with a varying drift term bounded in LN 维数为 N 的椭圆问题，其漂移项的变化在 LN 中有界
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-29 DOI: 10.3233/asy-241914
Juan Casado-Díaz
{"title":"An elliptic problem in dimension N with a varying drift term bounded in LN","authors":"Juan Casado-Díaz","doi":"10.3233/asy-241914","DOIUrl":"https://doi.org/10.3233/asy-241914","url":null,"abstract":"The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in LN(Ω), with N the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space H01(Ω). However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in (J. Differential Equations 258 (2015) 2290–2314), and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932520","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 asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion 通过马利亚文微积分的新渐近展开公式及其在分数布朗运动驱动的粗微分方程中的应用
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-13 DOI: 10.3233/asy-241910
Akihiko Takahashi, Toshihiro Yamada
{"title":"New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion","authors":"Akihiko Takahashi, Toshihiro Yamada","doi":"10.3233/asy-241910","DOIUrl":"https://doi.org/10.3233/asy-241910","url":null,"abstract":"This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate of the asymptotic expansion is shown under a weaker condition on the Malliavin covariance matrix of the target Wienerfunctional. In particular, the method provides a tractable expansion for the expectation of an irregular functional of the solution to a multidimensional rough differential equation driven by fractional Brownian motion with Hurst index H<1/2, without using complicated fractional integral calculus for the singular kernel. In a numerical experiment, our expansion shows a much better approximation for a probability distribution function than its normal approximation, which demonstrates the validity of the proposed method.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198668","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
Continuous data assimilation for the three dimensional primitive equations with magnetic field 带磁场的三维原始方程的连续数据同化
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-10 DOI: 10.3233/asy-241912
Yongqing Zhao, Wenjun Liu, Guangying Lv, Yuepeng Wang
{"title":"Continuous data assimilation for the three dimensional primitive equations with magnetic field","authors":"Yongqing Zhao, Wenjun Liu, Guangying Lv, Yuepeng Wang","doi":"10.3233/asy-241912","DOIUrl":"https://doi.org/10.3233/asy-241912","url":null,"abstract":"In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H2-strong solution of the assimilation system converges exponentially to the reference solution in the sense of L2 as t→∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity equation.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142198669","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
W 0 1 , p ( Ω ) × W 0 1 , p ( Ω ) versus C 0 1 ( Ω ) × C 0 1 ( Ω ) local minimizers W 0 1 , p ( Ω ) × W 0 1 , p ( Ω ) 对 C 0 1 ( Ω ) × C 0 1 ( Ω ) 的局部最小值
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-09 DOI: 10.3233/asy-241911
João Pablo P. Da Silva
{"title":"W 0 1 , p ( Ω ) × W 0 1 , p ( Ω ) versus C 0 1 ( Ω ) × C 0 1 ( Ω ) local minimizers","authors":"João Pablo P. Da Silva","doi":"10.3233/asy-241911","DOIUrl":"https://doi.org/10.3233/asy-241911","url":null,"abstract":"In this work, we consider a functional I : W 0 1 , p ( Ω ) × W 0 1 , p ( Ω ) → R of the form I ( u , v ) = 1 p ∫ Ω ( | ∇ u | p + | ∇ v | p ) d x − ∫ Ω H ( x , u ( x ) , v ( x ) ) d x where Ω ⊂ R N is a smooth bounded domain, max { | ∂ s H ( x , s , t ) | , | ∂ t H ( x , s , t ) | } ⩽ C ( 1 + | s | σ 1 − 1 + | t | σ 2 − 1 ) a.e. x ∈ Ω, for some C > 0, ∀ t , s ∈ R, p < σ i ⩽ p ∗ : = N p / ( N − p ), i = 1 , 2, and 1 < p < N. We prove that a local minimum in the topology of C 0 1 ( Ω ) × C 0 1 ( Ω ) is a local minimum in the topology of W 0 1 , p ( Ω ) × W 0 1 , p ( Ω ). An important application of this result is related to the question of multiplicity of solutions for a class of systems with concave-convex type nonlinearities.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140995918","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
Ground state solutions for generalized quasilinear Schrödinger equations 广义准薛定谔方程的基态解
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-05-02 DOI: 10.3233/asy-241913
Xiang-Dong Fang, Zhi-Qing Han
{"title":"Ground state solutions for generalized quasilinear Schrödinger equations","authors":"Xiang-Dong Fang, Zhi-Qing Han","doi":"10.3233/asy-241913","DOIUrl":"https://doi.org/10.3233/asy-241913","url":null,"abstract":"In this paper we consider the generalized quasilinear Schrödinger equations − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = h ( x , u ) , x ∈ R N , where V and h are periodic in x i , 1 ⩽ i ⩽ N. By using variational methods, we prove the existence of ground state solutions, i.e., nontrivial solutions with least possible energy.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141018125","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
Partial data inverse problems for magnetic Schrödinger operators on conformally transversally anisotropic manifolds 共形横向各向异性流形上磁薛定谔算子的部分数据逆问题
IF 1.4 4区 数学
Asymptotic Analysis Pub Date : 2024-04-29 DOI: 10.3233/asy-241909
Salem Selim, Lili Yan
{"title":"Partial data inverse problems for magnetic Schrödinger operators on conformally transversally anisotropic manifolds","authors":"Salem Selim, Lili Yan","doi":"10.3233/asy-241909","DOIUrl":"https://doi.org/10.3233/asy-241909","url":null,"abstract":"We study inverse boundary problems for the magnetic Schrödinger operator with Hölder continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n⩾3 with connected boundary. A global uniqueness result is established for magnetic fields and electric potentials from the partial Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508377","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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