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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":"3 1","pages":""},"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
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":"69 1","pages":""},"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
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":"32 1","pages":""},"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
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":"1 1","pages":""},"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":"75 1","pages":""},"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":"2013 1","pages":""},"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
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":"72 1","pages":""},"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
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":"31 1","pages":""},"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
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":"72 1","pages":""},"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
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":"57 1","pages":""},"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
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