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Interfaces and Free Boundaries最新文献

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Stability of self-similar solutions to geometric flows 几何流自相似解的稳定性
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-05-30 DOI: 10.4171/ifb/488
Hengrong Du, Nung Kwan Yip
{"title":"Stability of self-similar solutions to geometric flows","authors":"Hengrong Du, Nung Kwan Yip","doi":"10.4171/ifb/488","DOIUrl":"https://doi.org/10.4171/ifb/488","url":null,"abstract":"We show that self-similar solutions for the mean curvature flow, surface diffusion, and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipschitz norm. Roughly speaking, the perturbed solutions are asymptotically self-similar as time tends to infinity. Our results are built upon the global analytic solutions constructed by Koch and Lamm in 2012, the compactness arguments adapted by Asai and Giga in 2014, and the spatial equi-decay properties on certain weighted function spaces. The proof for all of the above flows are achieved in a unified framework by utilizing the estimates of the linearized operator.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"355 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135643219","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
Linear stability implies nonlinear stability for Faber–Krahn-type inequalities 线性稳定性意味着faber - krahn型不等式的非线性稳定性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-03-10 DOI: 10.4171/ifb/487
M. Allen, D. Kriventsov, Robin Neumayer
{"title":"Linear stability implies nonlinear stability for Faber–Krahn-type inequalities","authors":"M. Allen, D. Kriventsov, Robin Neumayer","doi":"10.4171/ifb/487","DOIUrl":"https://doi.org/10.4171/ifb/487","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87832861","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: 4
Eddy current approximation in Maxwell obstacle problems 麦克斯韦障碍问题中的涡流近似
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-12-08 DOI: 10.4171/ifb/486
Maurice Hensel, I. Yousept
{"title":"Eddy current approximation in Maxwell obstacle problems","authors":"Maurice Hensel, I. Yousept","doi":"10.4171/ifb/486","DOIUrl":"https://doi.org/10.4171/ifb/486","url":null,"abstract":". This paper analyzes the mathematical modeling of the transient eddy current approximation in the Maxwell obstacle problem. Here, the medium is assumed to be solely open, containing conducting and non-conducting materials with certain properties of anisotropy and non-smoothness. The proposed evolutionary PDE model preserves the Faraday law and excludes the displacement current from the governing Amp J ere–Maxwell variational inequality (VI). Our study strives to justify this model and delivers two main results: Global well-posedness of the model and its quantitative precision by uniform a priori estimates. The latter result yields an explicit bound for the smallness condition on the ratio between the electric permittivity and the electric conductivity in the region where the displacement current is disregarded. Below this threshold, the eddy current solution provides the desired reasonable approximation and justifies the proposed model.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"11 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84267792","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
Existence and stability of strong solutions to the Abels–Garcke–Grün model in three dimensions 三维abels - garcke - gr<s:1>模型强解的存在性与稳定性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-09-19 DOI: 10.4171/ifb/482
A. Giorgini
{"title":"Existence and stability of strong solutions to the Abels–Garcke–Grün model in three dimensions","authors":"A. Giorgini","doi":"10.4171/ifb/482","DOIUrl":"https://doi.org/10.4171/ifb/482","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"325 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76361488","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: 6
On the Rayleigh–Taylor instability for the two-phase Navier–Stokes equations in cylindrical domains 圆柱域两相Navier-Stokes方程的Rayleigh-Taylor不稳定性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-08-23 DOI: 10.4171/ifb/480
M. Wilke
{"title":"On the Rayleigh–Taylor instability for the two-phase Navier–Stokes equations in cylindrical domains","authors":"M. Wilke","doi":"10.4171/ifb/480","DOIUrl":"https://doi.org/10.4171/ifb/480","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"20 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84235832","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 of nonnegative solutions to stochastic thin-film equations in two space dimensions 二维随机薄膜方程非负解的存在性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-08-05 DOI: 10.4171/ifb/476
S. Metzger, Günther Grün
{"title":"Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions","authors":"S. Metzger, Günther Grün","doi":"10.4171/ifb/476","DOIUrl":"https://doi.org/10.4171/ifb/476","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87940853","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: 8
Curve-shortening of open elastic curves with repelling endpoints: A minimizing movements approach 具有排斥端点的开放弹性曲线的曲线缩短:最小化运动方法
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-05-10 DOI: 10.4171/ifb/475
Rufat Badal
{"title":"Curve-shortening of open elastic curves with repelling endpoints: A minimizing movements approach","authors":"Rufat Badal","doi":"10.4171/ifb/475","DOIUrl":"https://doi.org/10.4171/ifb/475","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78529878","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
Bifurcations of spherically asymmetric solutions to an evolution equation for curves 一类曲线演化方程球不对称解的分岔
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-04-26 DOI: 10.4171/ifb/474
Takeo Sugai
{"title":"Bifurcations of spherically asymmetric solutions to an evolution equation for curves","authors":"Takeo Sugai","doi":"10.4171/ifb/474","DOIUrl":"https://doi.org/10.4171/ifb/474","url":null,"abstract":"We show that a certain non-local curvature flow for planar curves has non-trivial self-similar solutions with $n$-fold rotational symmetry, bifurcated from a trivial circular solution. Moreover, we show that the trivial solution is stable with respect to perturbations which keep the geometric center and the enclosed area, and that, for $n$ different from 3, the $n$-fold symmetric solution is stable with respect to perturbations which satisfy the same conditions as above and have the same symmetry as the solutions.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"58 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532059","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
The Ginzburg–Landau energy with a pinning term oscillating faster than the coherence length 具有钉住项的金兹堡-朗道能量振荡速度快于相干长度
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-03-30 DOI: 10.4171/ifb/495
M. Santos, Rémy Rodiac, E. Sandier
{"title":"The Ginzburg–Landau energy with a pinning term oscillating faster than the coherence length","authors":"M. Santos, Rémy Rodiac, E. Sandier","doi":"10.4171/ifb/495","DOIUrl":"https://doi.org/10.4171/ifb/495","url":null,"abstract":"The aim of this article is to study the magnetic Ginzburg-Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster than the coherence length (varepsilon>0) which is also the inverse of the Ginzburg-Landau parameter. We study both the case of a periodic potential and of a random stationary ergodic one. We prove that we can reduce the study of the problem to the case where the pinning term is replaced by its average, in the periodic case, and by its expectation with respect to the random parameter in the random case. In order to do that we use a decoupling of the energy due to Lassoued-Mironescu. This leads us to the study of the convergence of a scalar positive minimizer of the Ginzburg-Landau energy with pinning term and with homogeneous Neumann boundary conditions. We prove uniform convergence of this minimizer towards the mean value of the pinning term by using a blow-up argument and a Liouville type result for non-vanishing entire solutions of the real Ginzburg-Landau/Allen-Cahn equation, due to Farina.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85464088","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
Fully nonlinear free transmission problems with nonhomogeneous degeneracies 具有非齐次退化的全非线性自由传输问题
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2022-03-09 DOI: 10.4171/ifb/471
Cristiana De Filippis
{"title":"Fully nonlinear free transmission problems with nonhomogeneous degeneracies","authors":"Cristiana De Filippis","doi":"10.4171/ifb/471","DOIUrl":"https://doi.org/10.4171/ifb/471","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"106 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73425722","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: 4
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