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dc.contributor.authorBoldrini, Jose Luiz ( Orcid Icon 0000-0003-4293-7611 )
dc.contributor.authorDias Vaz, Cristina Lucia ( )
dc.date.accessioned2021-01-27T21:43:26Z
dc.date.available2021-01-27T21:43:26Z
dc.date.issued2003-11-03
dc.identifier.citationBoldrini, J. L., & Dias Vaz, C. L. (2003). Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions. Electronic Journal of Differential Equations, 2003(109), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13160
dc.description.abstractWe study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.en_US
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectPhase-fielden_US
dc.subjectPhase transitionsen_US
dc.subjectSolidificationen_US
dc.subjectConvectionen_US
dc.subjectNavier-Stokes equationsen_US
dc.titleExistence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensionsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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