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Interfaces and Free Boundaries最新文献

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A bulk-surface reaction-diffusion system for cell polarization 电池极化的本体-表面反应-扩散系统
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2019-02-15 DOI: 10.4171/ifb/433
B. Niethammer, M. Roger, J. Vel'azquez
{"title":"A bulk-surface reaction-diffusion system for cell polarization","authors":"B. Niethammer, M. Roger, J. Vel'azquez","doi":"10.4171/ifb/433","DOIUrl":"https://doi.org/10.4171/ifb/433","url":null,"abstract":"We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in certain parameter regimes in which several reaction rates on the membrane as well as the diffusion coefficient within the cell are large. It turns out that in suitable scaling limits steady states converge to solutions of some obstacle type problems. For these limiting problems we prove the onset of polarization if the total mass of protein is sufficiently small. For some variants we can even characterize precisely the critical mass for which polarization occurs.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"96 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2019-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90742685","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: 9
On the entropy of parabolic Allen–Cahn equation 关于抛物型Allen-Cahn方程的熵
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-12-20 DOI: 10.4171/ifb/460
Ao Sun
{"title":"On the entropy of parabolic Allen–Cahn equation","authors":"Ao Sun","doi":"10.4171/ifb/460","DOIUrl":"https://doi.org/10.4171/ifb/460","url":null,"abstract":"In this paper we define the entropy of Radon measures, especially the measures associated to the parabolic Allen-Cahn equation. We show that when the entropy of the initial data is small enough (less than twice of the energy of the one dimensional standing wave), the limit measure of the parabolic Allen-Cahn equation has unit density.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"44 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72476446","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
Free boundary regularity for a degenerate problem with right hand side 一类带右手边的退化问题的自由边界正则性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-12-13 DOI: 10.4171/IFB/413
R. Leitão, G. Ricarte
{"title":"Free boundary regularity for a degenerate problem with right hand side","authors":"R. Leitão, G. Ricarte","doi":"10.4171/IFB/413","DOIUrl":"https://doi.org/10.4171/IFB/413","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83082861","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
Approximation of minimal surfaces with free boundaries 具有自由边界的最小曲面的逼近
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-12-13 DOI: 10.4171/IFB/412
U. Dierkes, Tristan Jenschke, Paola Pozzi
{"title":"Approximation of minimal surfaces with free boundaries","authors":"U. Dierkes, Tristan Jenschke, Paola Pozzi","doi":"10.4171/IFB/412","DOIUrl":"https://doi.org/10.4171/IFB/412","url":null,"abstract":"In this paper we develop a penalty method to approximate solutions of the free boundary problem for minimal surfaces. To this end we study the problem of finding minimizers of a functional Fλ which is defined as the sum of the Dirichlet integral and an appropriate penalty term weighted by a parameter λ. We prove existence of a solution for λ large enough as well as convergence to a solution of the free boundary problem as λ tends to infinity. Additionally regularity at the boundary of these solutions is shown, which is crucial for deriving numerical error estimates. Since every solution is harmonic, the analysis may be largely simplified by considering boundary values only and using harmonic extensions. In a subsequent paper we develop a fully discrete finite element procedure for approximating solutions to this one-dimensional problem and prove an error estimate which includes an order of convergence with respect to the grid size.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89282039","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
An obstacle problem for elastic curves: Existence results 弹性曲线的障碍问题:存在性结果
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-12-07 DOI: 10.4171/IFB/418
Marius Muller
{"title":"An obstacle problem for elastic curves: Existence results","authors":"Marius Muller","doi":"10.4171/IFB/418","DOIUrl":"https://doi.org/10.4171/IFB/418","url":null,"abstract":"We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in a way that an existence result can be obtained by a penalization argument.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"30 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81609820","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
Schwarz P surfaces and a non local perturbation of the perimeter Schwarz P曲面和周长的非局部摄动
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-11-05 DOI: 10.4171/IFB/404
M. Rizzi
{"title":"Schwarz P surfaces and a non local perturbation of the perimeter","authors":"M. Rizzi","doi":"10.4171/IFB/404","DOIUrl":"https://doi.org/10.4171/IFB/404","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"7 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79727727","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
A limit case in non-isotropic two-phase minimization problems driven by $p$-Laplacians 由拉普拉斯算子驱动的非各向同性两相极小化问题的极限情况
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-11-05 DOI: 10.4171/IFB/406
J. V. Silva, J. Rossi
{"title":"A limit case in non-isotropic two-phase minimization problems driven by $p$-Laplacians","authors":"J. V. Silva, J. Rossi","doi":"10.4171/IFB/406","DOIUrl":"https://doi.org/10.4171/IFB/406","url":null,"abstract":"In this work we study a minimization problem with two-phases where in each phase region the problem is ruled by a quasi-linear elliptic operator of p−Laplacian type. The problem in its variational form is as follows: min v  ∫ Ω∩{v>0} ( 1 p |∇v|p +λ p +(x)+ f+(x)v ) dx+ ∫ Ω∩{v≤0} ( 1 q |∇v|q +λ q −(x)+ f−(x)v ) dx  . Here we minimize among all admissible functions v in an appropriate Sobolev space with a prescribed boundary datum v = g on ∂Ω. First, we show existence of a minimizer, prove some properties, and provide an example for non-uniqueness. Moreover, we analyze the limit case where p and q go to infinity, obtaining a limiting free boundary problem governed by the ∞−Laplacian operator. Consequently, Lipschitz regularity for any limiting solution is obtained. Finally, we establish some weak geometric properties for solutions.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"8 1","pages":"379-406"},"PeriodicalIF":1.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87145981","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: 3
Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity 超导平均场理论中自由边界与固定边界的非横向相交
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-10-20 DOI: 10.4171/IFB/423
E. Indrei
{"title":"Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity","authors":"E. Indrei","doi":"10.4171/IFB/423","DOIUrl":"https://doi.org/10.4171/IFB/423","url":null,"abstract":"Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean-field theory of superconducting vortices.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"62 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/IFB/423","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72395231","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
Global weak solvability, continuous dependence on data, and large time growth of swelling moving interfaces 整体弱可解性，对数据的持续依赖，膨胀移动界面增长时间大
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-10-18 DOI: 10.4171/ifb/431
K. Kumazaki, A. Muntean
{"title":"Global weak solvability, continuous dependence on data, and large time growth of swelling moving interfaces","authors":"K. Kumazaki, A. Muntean","doi":"10.4171/ifb/431","DOIUrl":"https://doi.org/10.4171/ifb/431","url":null,"abstract":"We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend continuously on data and parameters. The key observation is that the structure of our system of partial differential equations allows us to show that the moving a priori unknown interface never disappears. As main ingredients of the global existence proof, we rely on a local weak solvability result for our problem, uniform estimates of the solution, integral estimates on quantities defined at the free boundary, as well as a fine pointwise lower bound for the position of the moving boundary. Some of the estimates are time-independent. They allow us to explore the large time behavior of the position of the moving boundary. The approach is specific to one-dimensional settings.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89475397","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
A convex approach to the Gilbert–Steiner problem 吉尔伯特-斯坦纳问题的一个凸方法
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2018-10-12 DOI: 10.4171/ifb/436
M. Bonafini, 'Edouard Oudet
{"title":"A convex approach to the Gilbert–Steiner problem","authors":"M. Bonafini, 'Edouard Oudet","doi":"10.4171/ifb/436","DOIUrl":"https://doi.org/10.4171/ifb/436","url":null,"abstract":"We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in [9], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2018-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84743562","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: 5
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