Interfaces and Free Boundaries最新文献

筛选
英文 中文
A diffuse interface model of tumour evolution under a finite elastic confinement 有限弹性约束下肿瘤演化的扩散界面模型
4区 数学
Interfaces and Free Boundaries Pub Date : 2024-05-08 DOI: 10.4171/ifb/520
Abramo Agosti, Riccardo Bardin, Pasquale Ciarletta, Maurizio Grasselli
{"title":"A diffuse interface model of tumour evolution under a finite elastic confinement","authors":"Abramo Agosti, Riccardo Bardin, Pasquale Ciarletta, Maurizio Grasselli","doi":"10.4171/ifb/520","DOIUrl":"https://doi.org/10.4171/ifb/520","url":null,"abstract":"Diffuse interface models have gained a growing interest in cancer research for their ability to investigate the mechano-biological features during tumour progression and to provide simulation tools for personalised anti-cancer strategies at an affordable computational cost. Here we propose a diffuse interface model for tumour evolution which accounts for an interfacial structure mimicking a finite elastic confinement at the tumour boundary, possibly due either to a localised elastic stress induced by host tissue displacements, or collagen remodelling in the peritumoural area. This model consists of a partial differential equation of the Cahn–Hilliard type, with degenerate mobility, single-well potential, and an elastic non-local term acting as the effect of a membrane confinement in the chemical potential. Using mixture theory, we derive the corresponding governing equations from thermodynamic principles based on realistic physical and biological assumptions. First, we introduce a suitable regularised problem in order to deal with the degeneracy set of the mobility and the singularity of the potential. For this problem we find a weak solution and provide a regularity result. Then, we establish suitable a priori estimates which are uniform with respect to the regularisation parameters. Passing to the limit in the regularised problem, we prove existence results for different classes of weak solutions to the original problem. Finally, we propose a continuous Galerkin Finite-Element discretisation of the problem, where the positivity of the discrete solution is enforced through a variational inequality. Numerical simulations in a two-dimensional domain are also discussed in three test cases for illustrative purposes.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"27 1","pages":"27-64"},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ems.press/content/serial-article-files/47647","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147910517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effective interface conditions for a porous medium type problem 多孔介质型问题的有效界面条件
4区 数学
Interfaces and Free Boundaries Pub Date : 2024-02-06 DOI: 10.4171/ifb/505
Giorgia Ciavolella, Noemi David, Alexandre Poulain
{"title":"Effective interface conditions for a porous medium type problem","authors":"Giorgia Ciavolella, Noemi David, Alexandre Poulain","doi":"10.4171/ifb/505","DOIUrl":"https://doi.org/10.4171/ifb/505","url":null,"abstract":"Motivated by biological applications on tumour invasion through thin membranes, we study a porous medium type equation where the density of the cell population evolves under Darcy’s law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the effective interface problem and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al. (2019), which are compatible with nonlinear generalized Kedem–Katchalsky ones. Our analysis relies on a priori estimates and compactness arguments as well as on the construction of a suitable extension operator, which allows us to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"26 2","pages":"161-188"},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ems.press/content/serial-article-files/39265","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147896345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Quantitative convergence of the ``bulk'' free boundary in an oscillatory obstacle problem 振荡障碍问题中 "大块 "自由边界的定量收敛性
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-12-21 DOI: 10.4171/ifb/501
Farhan Abedin, William M. Feldman
{"title":"Quantitative convergence of the ``bulk'' free boundary in an oscillatory obstacle problem","authors":"Farhan Abedin, William M. Feldman","doi":"10.4171/ifb/501","DOIUrl":"https://doi.org/10.4171/ifb/501","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"48 24","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138952610","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 two-phase free boundary with a logarithmic term 带有对数项的两相自由边界
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-11-22 DOI: 10.4171/ifb/502
Morteza Fotouhi, Somayeh Khademloo
{"title":"A two-phase free boundary with a logarithmic term","authors":"Morteza Fotouhi, Somayeh Khademloo","doi":"10.4171/ifb/502","DOIUrl":"https://doi.org/10.4171/ifb/502","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248428","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
Embeddedness of liquid-vapour interfaces in stable equilibrium 稳定平衡中液-气界面的嵌入性
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-19 DOI: 10.4171/ifb/490
Costante Bellettini
{"title":"Embeddedness of liquid-vapour interfaces in stable equilibrium","authors":"Costante Bellettini","doi":"10.4171/ifb/490","DOIUrl":"https://doi.org/10.4171/ifb/490","url":null,"abstract":"We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g., water) is subject to a volume constraint, it does not mix with the surrounding vapour (e.g., air), it may come into contact with solid supports (e.g., a container), and it is subject to the action of an analytic potential field (e.g., gravity). The region occupied by the liquid is described as a set of locally finite perimeter (Caccioppoli set) in $R^3$; no a priori regularity assumption is made on its boundary. The (twofold) scope in this note is to propose a weakest possible set of mathematical assumptions that sensibly describe a condition of stable equilibrium for the liquid-vapour interface (the capillary surface), and to infer from those that this interface is a smoothly embedded analytic surface. (The liquid-solid-vapour junction, or free boundary, can be present but is not analysed here.) The result relies fundamentally on the recent varifold regularity theory developed by the author and Wickramasekera, and on the identification of a suitable formulation of the stability condition.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666551","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
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation 运动薄域热方程及其极限方程经典解的误差估计
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-13 DOI: 10.4171/ifb/499
Tatsu-Hiko Miura
{"title":"Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation","authors":"Tatsu-Hiko Miura","doi":"10.4171/ifb/499","DOIUrl":"https://doi.org/10.4171/ifb/499","url":null,"abstract":"We consider the Neumann-type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918853","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 novel finite element approximation of anisotropic curve shortening flow 各向异性曲线缩短流的一种新的有限元逼近
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-10-07 DOI: 10.4171/ifb/500
Klaus Deckelnick, Robert Nürnberg
{"title":"A novel finite element approximation of anisotropic curve shortening flow","authors":"Klaus Deckelnick, Robert Nürnberg","doi":"10.4171/ifb/500","DOIUrl":"https://doi.org/10.4171/ifb/500","url":null,"abstract":"We extend the DeTurck trick from the classical isotropic curve shortening flow to the anisotropic setting. Here, the anisotropic energy density is allowed to depend on space, which allows an interpretation in the context of Finsler metrics, giving rise to, for instance, geodesic curvature flow in Riemannian manifolds. Assuming that the density is strictly convex and smooth, we introduce a novel weak formulation for anisotropic curve shortening flow. We then derive an optimal $H^1$-error bound for a continuous-in-time semidiscrete finite element approximation that uses piecewise linear elements. In addition, we consider some fully practical fully discrete schemes and prove their unconditional stability. Finally, we present several numerical simulations, including some convergence experiments that confirm the derived error bound, as well as applications to crystalline curvature flow and geodesic curvature flow.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135252054","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
Classification of global solutions of a free boundary problem in the plane 平面上自由边界问题整体解的分类
4区 数学
Interfaces and Free Boundaries Pub Date : 2023-09-13 DOI: 10.4171/ifb/494
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci
{"title":"Classification of global solutions of a free boundary problem in the plane","authors":"Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci","doi":"10.4171/ifb/494","DOIUrl":"https://doi.org/10.4171/ifb/494","url":null,"abstract":"We classify non-trivial, non-negative, positively homogeneous solutions of the equation $$ Delta u=gamma u^{gamma-1} $$ in the plane. The problem is motivated by the analysis of the classical Alt–Phillips free boundary problem, but considered here with negative exponents $gamma$. The proof relies on several bespoke results for ordinary differential equations.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690247","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
Instantaneous convexity breaking for the quasi-static droplet model 准静态液滴模型的瞬时凸破缺
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-08-15 DOI: 10.4171/ifb/498
Albert Chau, B. Weinkove
{"title":"Instantaneous convexity breaking for the quasi-static droplet model","authors":"Albert Chau, B. Weinkove","doi":"10.4171/ifb/498","DOIUrl":"https://doi.org/10.4171/ifb/498","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87993911","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 全非线性自由传输问题
IF 1 4区 数学
Interfaces and Free Boundaries Pub Date : 2023-06-02 DOI: 10.4171/ifb/489
Edgard A. Pimentel, Makson S. Santos
{"title":"Fully nonlinear free transmission problems","authors":"Edgard A. Pimentel, Makson S. Santos","doi":"10.4171/ifb/489","DOIUrl":"https://doi.org/10.4171/ifb/489","url":null,"abstract":"","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79427418","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
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信
小红书