Asymptotic Analysis最新文献

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Existence and non-existence results to a mixed anisotropic Schrödinger system in a plane 平面内混合各向异性薛定谔系统的存在与不存在结果
Asymptotic Analysis Pub Date : 2024-07-11 DOI: 10.3233/asy-241922
H. Hajaiej, Rohit Kumar, Tuhina Mukherjee, Linjie Song
{"title":"Existence and non-existence results to a mixed anisotropic Schrödinger system in a plane","authors":"H. Hajaiej, Rohit Kumar, Tuhina Mukherjee, Linjie Song","doi":"10.3233/asy-241922","DOIUrl":"https://doi.org/10.3233/asy-241922","url":null,"abstract":"This article focuses on the existence and non-existence of solutions for the following system of local and nonlocal type − ∂ x x u + ( − Δ ) y s 1 u + u − u 2 s 1 − 1 = κ α h ( x , y ) u α − 1 v β in  R 2 , − ∂ x x v + ( − Δ ) y s 2 v + v − v 2 s 2 − 1 = κ β h ( x , y ) u α v β − 1 in  R 2 , u , v ⩾ 0 in  R 2 , where s 1 , s 2 ∈ ( 0 , 1 ) , α, β > 1, α + β ⩽ min { 2 s 1 , 2 s 2 }, and 2 s i = 2 ( 1 + s i ) 1 − s i , i = 1 , 2. The existence of a ground state solution entirely depends on the behaviour of the parameter κ > 0 and on the function h. In this article, we prove that a ground state solution exists in the subcritical case if κ is large enough and h satisfies (H). Further, if κ becomes very small, then there is no solution to our system. The study of the critical case, i.e., s 1 = s 2 = s, α + β = 2 s , is more complex, and the solution exists only for large κ and radial h satisfying (H1). Finally, we establish a Pohozaev identity which enables us to prove the non-existence results under some smooth assumptions on h.","PeriodicalId":505560,"journal":{"name":"Asymptotic Analysis","volume":"32 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141658673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic expansion of thick distributions II 厚分布的渐近展开 II
Asymptotic Analysis Pub Date : 2024-07-11 DOI: 10.3233/asy-241924
Jiajia Ding, Ricardo Estrada, Yunyun Yang
{"title":"Asymptotic expansion of thick distributions II","authors":"Jiajia Ding, Ricardo Estrada, Yunyun Yang","doi":"10.3233/asy-241924","DOIUrl":"https://doi.org/10.3233/asy-241924","url":null,"abstract":"In this article we continue our research in (Yang and Estrada in Asymptot. Anal. 95(1–2) (2015) 1–19), about the asymptotic expansion of thick distributions. We compute more examples of asymptotic expansion of integral transforms using the techniques developed in (Yang and Estrada in Asymptot. Anal. 95(1–2) (2015) 1–19). Besides, we derive a new “Laplace Formula” for the situation in which a point singularity is allowed.","PeriodicalId":505560,"journal":{"name":"Asymptotic Analysis","volume":"15 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141656170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The time horizon for stochastic homogenization of the one-dimensional wave equation 一维波方程随机均质化的时间范围
Asymptotic Analysis Pub Date : 2024-07-09 DOI: 10.3233/asy-241923
M. Schäffner, B. Schweizer
{"title":"The time horizon for stochastic homogenization of the one-dimensional wave equation","authors":"M. Schäffner, B. Schweizer","doi":"10.3233/asy-241923","DOIUrl":"https://doi.org/10.3233/asy-241923","url":null,"abstract":"The wave equation with stochastic rapidly oscillating coefficients can be classically homogenized on bounded time intervals; solutions converge in the homogenization limit to solutions of a wave equation with constant coefficients. This is no longer true on large time scales: Even in the periodic case with periodicity ε, classical homogenization fails for times of the order ε − 2 . We consider the one-dimensional wave equation with random rapidly oscillation coefficients on scale ε and are interested in the critical time scale ε − β from where on classical homogenization fails. In the general setting, we derive upper and lower bounds for β in terms of the growth rate of correctors. In the specific setting of i.i.d. coefficients with matched impedance, we show that the critical time scale is ε − 1 .","PeriodicalId":505560,"journal":{"name":"Asymptotic Analysis","volume":"84 21","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thin ferromagnetic plates with magnetostriction 具有磁致伸缩性的薄铁磁板
Asymptotic Analysis Pub Date : 2024-03-13 DOI: 10.3233/asy-241899
Mouna Kassan, Gilles Carbou, Mustapha Jazar
{"title":"Thin ferromagnetic plates with magnetostriction","authors":"Mouna Kassan, Gilles Carbou, Mustapha Jazar","doi":"10.3233/asy-241899","DOIUrl":"https://doi.org/10.3233/asy-241899","url":null,"abstract":"In this paper, we establish the existence of global-in-time weak solutions for the Landau–Lifschitz–Gilbert equation with magnetostriction in the case of mixed boundary conditions. From this model, we derive by asymptotic method a two-dimensional model for thin ferromagnetic plates taking into account magnetostrictive effects.","PeriodicalId":505560,"journal":{"name":"Asymptotic Analysis","volume":"568 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140246775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 class of elliptic equations with critical perturbations in the hyperbolic space 论双曲空间中一类具有临界扰动的椭圆方程
Asymptotic Analysis Pub Date : 2024-02-15 DOI: 10.3233/asy-241895
D. Ganguly, Diksha Gupta, K. Sreenadh
{"title":"On a class of elliptic equations with critical perturbations in the hyperbolic space","authors":"D. Ganguly, Diksha Gupta, K. Sreenadh","doi":"10.3233/asy-241895","DOIUrl":"https://doi.org/10.3233/asy-241895","url":null,"abstract":"We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space − Δ B N u − λ u = a ( x ) u p − 1 + ε u 2 ∗ − 1 in  B N , u ∈ H 1 ( B N ) , where B N denotes the hyperbolic space, 2 < p < 2 ∗ : = 2 N N − 2 , if N ⩾ 3 ; 2 < p < + ∞, if N = 2, λ < ( N − 1 ) 2 4 , and 0 < a ∈ L ∞ ( B N ). We first prove the existence of a positive radially symmetric ground-state solution for a ( x ) ≡ 1. Next, we prove that for a ( x ) ⩾ 1, there exists a ground-state solution for ε small. For proof, we employ “conformal change of metric” which allows us to transform the original equation into a singular equation in a ball in R N . Then by carefully analysing the energy level using blow-up arguments, we prove the existence of a ground-state solution. Finally, the case a ( x ) ⩽ 1 is considered where we first show that there is no ground-state solution, and prove the existence of a bound-state solution (high energy solution) for ε small. We employ variational arguments in the spirit of Bahri–Li to prove the existence of high energy-bound-state solutions in the hyperbolic space.","PeriodicalId":505560,"journal":{"name":"Asymptotic Analysis","volume":"9 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139962955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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