ON A CLASS OF GEOMETRY-DRIVEN FREE BOUNDAR PROBLEMS.
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| Title: | ON A CLASS OF GEOMETRY-DRIVEN FREE BOUNDAR PROBLEMS. |
|---|---|
| Authors: | Crowdy, Darren |
| Source: | SIAM Journal on Applied Mathematics. 2001, Vol. 62 Issue 3, p945. 20p. |
| Subjects: | Cauchy transform, Geometry problems & exercises, Partial differential equations, Mathematical transformations |
| Abstract: | An abstract class of two-dimensional geometry-driven free boundary problems is considered in which the evolution of the Cauchy transform of the time-evolving domain satisfies a partial differential equation of conservation type. This idea generalizes an association between free boundary problems and the inverse gravitational problem. It is shown that this class of free boundary problems admits exact solutions expressible in terms of a finite set of time-evolving parameters. In addition, even when exact solutions are not available, a theorem is established which shows that solutions corresponding to certain initial conditions possess nontrivial conserved quantities. Two distinct problems of physical interest are shown to fall within this abstract class: the evolution of a fluid blob in a rotating Hele-Shaw cell and the evolution of highly viscous fluid under the effects of surface tension. Various aspects of these two problems are discussed. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Applied Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 10195918 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: ON A CLASS OF GEOMETRY-DRIVEN FREE BOUNDAR PROBLEMS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Crowdy%2C+Darren%22">Crowdy, Darren</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Applied+Mathematics%22">SIAM Journal on Applied Mathematics</searchLink>. 2001, Vol. 62 Issue 3, p945. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Cauchy+transform%22">Cauchy transform</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry+problems+%26+exercises%22">Geometry problems & exercises</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An abstract class of two-dimensional geometry-driven free boundary problems is considered in which the evolution of the Cauchy transform of the time-evolving domain satisfies a partial differential equation of conservation type. This idea generalizes an association between free boundary problems and the inverse gravitational problem. It is shown that this class of free boundary problems admits exact solutions expressible in terms of a finite set of time-evolving parameters. In addition, even when exact solutions are not available, a theorem is established which shows that solutions corresponding to certain initial conditions possess nontrivial conserved quantities. Two distinct problems of physical interest are shown to fall within this abstract class: the evolution of a fluid blob in a rotating Hele-Shaw cell and the evolution of highly viscous fluid under the effects of surface tension. Various aspects of these two problems are discussed. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Applied Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=10195918 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 945 Subjects: – SubjectFull: Cauchy transform Type: general – SubjectFull: Geometry problems & exercises Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Mathematical transformations Type: general Titles: – TitleFull: ON A CLASS OF GEOMETRY-DRIVEN FREE BOUNDAR PROBLEMS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Crowdy, Darren IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: 2001 Type: published Y: 2001 Identifiers: – Type: issn-print Value: 00361399 Numbering: – Type: volume Value: 62 – Type: issue Value: 3 Titles: – TitleFull: SIAM Journal on Applied Mathematics Type: main |
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