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Interfaces and Free Boundaries最新文献

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Derivation of a heteroepitaxial thin-film model 异质外延薄膜模型的推导
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-09-19 DOI: 10.4171/ifb/435
E. Davoli, Paolo Piovano
{"title":"Derivation of a heteroepitaxial thin-film model","authors":"E. Davoli, Paolo Piovano","doi":"10.4171/ifb/435","DOIUrl":"https://doi.org/10.4171/ifb/435","url":null,"abstract":"A variational model for epitaxially-strained thin films on rigid substrates is derived both by {Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for regular configurations. The model is characterized by a configurational energy that accounts for both the competing mechanisms responsible for the film shape. On the one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations may be present because film atoms move to release the elastic energy. On the other hand, flatter profiles may be preferable to minimize the surface energy. Some first regularity results are presented for energetically-optimal film profiles.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79715956","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: 11
A homogenization result in the gradient theory of phase transitions 均匀化导致相变梯度理论
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-08-06 DOI: 10.4171/IFB/426
R. Cristoferi, I. Fonseca, Adrian Hagerty, Cristina Popovici
{"title":"A homogenization result in the gradient theory of phase transitions","authors":"R. Cristoferi, I. Fonseca, Adrian Hagerty, Cristina Popovici","doi":"10.4171/IFB/426","DOIUrl":"https://doi.org/10.4171/IFB/426","url":null,"abstract":"A homogenization problem arising in the gradient theory of ∞uid-∞uid phase transitions is addressed in the vector-valued setting by means of i-convergence.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74843487","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: 15
Quantitative analysis of finite-difference approximations of free-discontinuity problems 自由不连续问题有限差分近似的定量分析
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-07-14 DOI: 10.4171/ifb/443
Annika Bach, Andrea Braides, C. Zeppieri
{"title":"Quantitative analysis of finite-difference approximations of free-discontinuity problems","authors":"Annika Bach, Andrea Braides, C. Zeppieri","doi":"10.4171/ifb/443","DOIUrl":"https://doi.org/10.4171/ifb/443","url":null,"abstract":"Motivated by applications to image reconstruction, in this paper we analyse a emph{finite-difference discretisation} of the Ambrosio-Tortorelli functional. Denoted by $varepsilon$ the elliptic-approximation parameter and by $delta$ the discretisation step-size, we fully describe the relative impact of $varepsilon$ and $delta$ in terms of $Gamma$-limits for the corresponding discrete functionals, in the three possible scaling regimes. We show, in particular, that when $varepsilon$ and $delta$ are of the same order, the underlying lattice structure affects the $Gamma$-limit which turns out to be an anisotropic free-discontinuity functional.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72962470","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: 12
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type 活化剂-抑制剂型反应-扩散体系中多尺度模式形成级联
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-07-09 DOI: 10.4171/IFB/403
M. Henry, D. Hilhorst, C. Muratov
{"title":"A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type","authors":"M. Henry, D. Hilhorst, C. Muratov","doi":"10.4171/IFB/403","DOIUrl":"https://doi.org/10.4171/IFB/403","url":null,"abstract":"A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in R , with N ≥ 2. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the considered class of reaction-diffusion equations. ∗CMI Université d’Aix-Marseille, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13, France †Laboratoire de Mathématiques, CNRS and University Paris-Sud Paris-Saclay, 91405 Orsay Cedex, France ‡Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74132834","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: 2
Bubbles and droplets in a singular limit of the FitzHugh–Nagumo system FitzHugh-Nagumo系统奇异极限中的气泡和液滴
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-07-09 DOI: 10.4171/IFB/400
Chao-Nien Chen, Yung-Sze Choi, Xiaofeng Ren
{"title":"Bubbles and droplets in a singular limit of the FitzHugh–Nagumo system","authors":"Chao-Nien Chen, Yung-Sze Choi, Xiaofeng Ren","doi":"10.4171/IFB/400","DOIUrl":"https://doi.org/10.4171/IFB/400","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81700897","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: 14
Well-posedness of non-isentropic Euler equations with physical vacuum 具有物理真空的非等熵欧拉方程的适定性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-06-26 DOI: 10.4171/IFB/422
Yong-cai Geng, Yachun Li, Dehua Wang, Runzhang Xu
{"title":"Well-posedness of non-isentropic Euler equations with physical vacuum","authors":"Yong-cai Geng, Yachun Li, Dehua Wang, Runzhang Xu","doi":"10.4171/IFB/422","DOIUrl":"https://doi.org/10.4171/IFB/422","url":null,"abstract":"We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the distance to the vacuum boundary. The main difficulty lies in the fact that the system of hyperbolic conservation laws becomes characteristic and degenerate at the vacuum boundary. Our proof is based on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term. Then we construct the solutions to this degenerate parabolic problem and establish the estimates that are uniform with respect to the artificial viscosity parameter. Solutions to the compressible Euler equations are obtained as the limit of the vanishing artificial viscosity. \u0000Different from the isentropic case cite{Coutand4, Lei}, our momentum equation of conservation laws has an extra term $p_{S}S_x$ that leads to some extra terms in the energy function and causes more difficulties even for the case of $gamma=2$. Moreover, we deal with this free boundary problem starting from the general cases of $2leqgamma<3$ and $1<gamma<2 $ instead of only emphasizing the isentropic case of $gamma=2$ in cite{Coutand4, jang1, Lei}.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84659522","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
Convergence of the Allen–Cahn equation to the mean curvature flow with 90o-contact angle in 2D Allen-Cahn方程对二维90°接触角平均曲率流的收敛性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-06-06 DOI: 10.4171/ifb/425
H. Abels, M. Moser
{"title":"Convergence of the Allen–Cahn equation to the mean curvature flow with 90o-contact angle in 2D","authors":"H. Abels, M. Moser","doi":"10.4171/ifb/425","DOIUrl":"https://doi.org/10.4171/ifb/425","url":null,"abstract":"We consider the sharp interface limit of the Allen-Cahn equation with homogeneous Neumann boundary condition in a two-dimensional domain $Omega$, in the situation where an interface has developed and intersects $partialOmega$. Here a parameter $varepsilon>0$ in the equation, which is related to the thickness of the diffuse interface, is sent to zero. The limit problem is given by mean curvature flow with a $90$textdegree-contact angle condition and convergence using strong norms is shown for small times. Here we assume that a smooth solution to this limit problem exists on $[0,T]$ for some $T>0$ and that it can be parametrized suitably. With the aid of asymptotic expansions we construct an approximate solution for the Allen-Cahn equation and estimate the difference of the exact and approximate solution with the aid of a spectral estimate for the linearized Allen-Cahn operator.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74481405","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
Global stability for solutions to the exponential PDE describing epitaxial growth 描述外延生长的指数PDE解的全局稳定性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-05-06 DOI: 10.4171/IFB/417
Jian‐Guo Liu, Robert M. Strain
{"title":"Global stability for solutions to the exponential PDE describing epitaxial growth","authors":"Jian‐Guo Liu, Robert M. Strain","doi":"10.4171/IFB/417","DOIUrl":"https://doi.org/10.4171/IFB/417","url":null,"abstract":"In this paper we prove the global existence, uniqueness, optimal large time decay rates, and uniform gain of analyticity for the exponential PDE $h_t=Delta e^{-Delta h}$ in the whole space $mathbb{R}^d_x$. We assume the initial data is of medium size in the critical Wiener algebra $Delta h in A(mathbb{R}^d)$. This exponential PDE was derived in (Krug, Dobbs, and Majaniemi in 1995) and more recently in (Marzuola and Weare 2013).","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74166881","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: 20
Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes 具有不同加载-卸载机制的内聚界面准静态H^1演化的逼近与表征
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-05-03 DOI: 10.4171/IFB/396
M. Negri, E. Vitali
{"title":"Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes","authors":"M. Negri, E. Vitali","doi":"10.4171/IFB/396","DOIUrl":"https://doi.org/10.4171/IFB/396","url":null,"abstract":"Abstract. We consider the quasi-static evolution of a prescribed cohesive interface: dissipative under loading and elastic under unloading. We provide existence in terms of parametrized BV evolutions, employing a discrete scheme based on local minimization, with respect to the Hnorm, of a regularized energy. Technically, the evolution is fully characterized by: equilibrium, energy balance and Karush-Kuhn-Tucker conditions for the internal variable. Catastrophic regimes (discontinuities in time) are described by gradient flows of visco-elastic type.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79556762","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: 10
Large time behavior of a two phase extension of the porous medium equation 多孔介质方程两相扩展的大时间行为
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-03-28 DOI: 10.4171/IFB/421
A. Oulhaj, C. Cancès, C. Chainais-Hillairet, Philippe Laurencçot
{"title":"Large time behavior of a two phase extension of the porous medium equation","authors":"A. Oulhaj, C. Cancès, C. Chainais-Hillairet, Philippe Laurencçot","doi":"10.4171/IFB/421","DOIUrl":"https://doi.org/10.4171/IFB/421","url":null,"abstract":"We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to identify the self-similar solutions that correspond to steady states of a rescaled version of the problem. We fully characterize the unique steady states that are identified as minimizers of a convex energy and shown to be radially symmetric. Moreover, we prove the convergence of the solution to the time-dependent model towards the unique stationary state as time goes to infinity. We finally provide numerical illustrations of the stationary states and we exhibit numerical convergence rates.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2018-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80562108","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: 7
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