Pub Date : 2019-11-11DOI: 10.1201/9780203755518-28
G. Georgiou, A. Boudouvis
{"title":"Singular Finite Element Solutions of the Axisymmetric Extrudate-Swell Problem","authors":"G. Georgiou, A. Boudouvis","doi":"10.1201/9780203755518-28","DOIUrl":"https://doi.org/10.1201/9780203755518-28","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83760758","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}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-12
N. Kenmochi, M. Kubo
{"title":"Well-Posedness for a Phase-Field Model with Constraint","authors":"N. Kenmochi, M. Kubo","doi":"10.1201/9780203755518-12","DOIUrl":"https://doi.org/10.1201/9780203755518-12","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79105128","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}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-22
V. Alexiades
Most models of alloy solidiication are severely limited by the assumption of constant density, thus excluding all convective eeects. We present a thermodynamicaly consistent model for binary alloy solidiication that incorporates energy, species and momentum conservation, constitutional supercooling, as well as temperature, concentration, and pressure dependence of thermophysical parameters. The crucial aspect is the development of an Equation of State capturing the thermochemistry of the phases. A numerical algorithm will also be outlined.
{"title":"Alloy Solidification with Convection in the Melt","authors":"V. Alexiades","doi":"10.1201/9780203755518-22","DOIUrl":"https://doi.org/10.1201/9780203755518-22","url":null,"abstract":"Most models of alloy solidiication are severely limited by the assumption of constant density, thus excluding all convective eeects. We present a thermodynamicaly consistent model for binary alloy solidiication that incorporates energy, species and momentum conservation, constitutional supercooling, as well as temperature, concentration, and pressure dependence of thermophysical parameters. The crucial aspect is the development of an Equation of State capturing the thermochemistry of the phases. A numerical algorithm will also be outlined.","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78722250","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}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-20
J. Rodrigues, J. M. Urbano
{"title":"On the Mathematical Analysis of a Valley Glacier Model","authors":"J. Rodrigues, J. M. Urbano","doi":"10.1201/9780203755518-20","DOIUrl":"https://doi.org/10.1201/9780203755518-20","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90978013","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}
{"title":"Overview of Dynamical Simulations of the Flow of Suspensions of Liquid Capsules and Drops","authors":"C. Pozrikidis","doi":"10.1201/9780203755518-6","DOIUrl":"https://doi.org/10.1201/9780203755518-6","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75822986","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}
Pub Date : 2019-01-01DOI: 10.1201/9780203755518-16
K. Hutter
{"title":"Mathematical Foundation of Ice Sheet and Ice Shelf Dynamics. A Physicist’s View","authors":"K. Hutter","doi":"10.1201/9780203755518-16","DOIUrl":"https://doi.org/10.1201/9780203755518-16","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73151317","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}
Pub Date : 2019-01-01DOI: 10.1201/9780203755518-23
J. Dold, I. Athanasopoulos, M. Makrakis, JF Rodrigues
{"title":"Implications of Non-Monotonic Curvature-Dependence in the Propagation Speed of an Interface","authors":"J. Dold, I. Athanasopoulos, M. Makrakis, JF Rodrigues","doi":"10.1201/9780203755518-23","DOIUrl":"https://doi.org/10.1201/9780203755518-23","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73756178","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}
Pub Date : 2019-01-01DOI: 10.1201/9780203755518-30
R. Kornhuber
A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constrained Newton type linearization. While convex min- imization provides global convergence of the overall iteration, the subsequent constrained Newton type linearization is intended to accelerate the conver- gence speed. We present a general convergence theory and discuss several applications.
{"title":"Monotone Iterations for Elliptic Variational Inequalities","authors":"R. Kornhuber","doi":"10.1201/9780203755518-30","DOIUrl":"https://doi.org/10.1201/9780203755518-30","url":null,"abstract":"A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constrained Newton type linearization. While convex min- imization provides global convergence of the overall iteration, the subsequent constrained Newton type linearization is intended to accelerate the conver- gence speed. We present a general convergence theory and discuss several applications.","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75261439","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}
Pub Date : 2019-01-01DOI: 10.1201/9780203755518-11
Björn Gustafsson, M. Putinar
We investigate the basic properties of the exponential transform E(z, w) = exp 7r 0 x dA(~) -) ) (z, w E C) of a domain Q c C and compute it in some simple cases. The main result states that if the Cauchy trans- form of the characteristic function of Q has an analytic continuation from C B S2 across aS2 then the same is true for E(z, w), in both variables. If F (z, w) de- notes this analytic-antianalytic continuation it follows that 8 Q is contained in a real analytic set, namely the zero set of F (z, z). This gives a new approach to the regularity theory for free boundaries in two dimensions.
研究了定义域Q C C的指数变换E(z, w) = exp 7r 0 x dA(~) -) (z, w E C)的基本性质，并在一些简单的情况下进行了计算。主要结果表明，如果Q的特征函数的柯西变换具有从C B S2到aS2的解析延拓，那么在两个变量中E(z, w)也是如此。如果F (z, w)注意到这个解析-反解析延拓，则8q包含在一个实解析集合中，即F (z, z)的零集中。这为二维自由边界的正则性理论提供了一个新的途径。
{"title":"An Exponential Transform and Regularity of Free Boundaries in Two Dimensions","authors":"Björn Gustafsson, M. Putinar","doi":"10.1201/9780203755518-11","DOIUrl":"https://doi.org/10.1201/9780203755518-11","url":null,"abstract":"We investigate the basic properties of the exponential transform E(z, w) = exp 7r 0 x dA(~) -) ) (z, w E C) of a domain Q c C and compute it in some simple cases. The main result states that if the Cauchy trans- form of the characteristic function of Q has an analytic continuation from C B S2 across aS2 then the same is true for E(z, w), in both variables. If F (z, w) de- notes this analytic-antianalytic continuation it follows that 8 Q is contained in a real analytic set, namely the zero set of F (z, z). This gives a new approach to the regularity theory for free boundaries in two dimensions.","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"147 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82623992","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}
Pub Date : 2019-01-01DOI: 10.1201/9780203755518-27
J. I. Díaz, E. Schiavi
{"title":"On a Degenerate System in Glaciology Giving Rise to a Free Boundary","authors":"J. I. Díaz, E. Schiavi","doi":"10.1201/9780203755518-27","DOIUrl":"https://doi.org/10.1201/9780203755518-27","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73623974","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}
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