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dc.contributor.authorLeFloch, Philippe ( )
dc.contributor.authorThanh, Mai Duc ( )
dc.date.accessioned2019-12-20T20:48:47Z
dc.date.available2019-12-20T20:48:47Z
dc.date.issued2000-12-01
dc.identifier.citationLeFloch, P. G., & Thanh, M. D. (2000). Nonclassical Riemann solvers and kinetic relations III: A nonconvex hyperbolic model for Van der Waals fluids. Electronic Journal of Differential Equations, 2000(72), pp. 1-19.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/9126
dc.description.abstractThis paper deals with the so-called p-system describing the dynamics of isothermal and compressible fluids. The constitutive equation is assumed to have the typical convexity/concavity properties of the van der Waals equation. We search for discontinuous solutions constrained by the associated mathematical entropy inequality. First, following a strategy proposed by Abeyaratne and Knowles and by Hayes and LeFloch, we describe here the whole family of nonclassical Riemann solutions for this model. Second, we supplement the set of equations with a kinetic relation for the propagation of nonclassical undercompressive shocks, and we arrive at a uniquely defined solution of the Riemann problem. We also prove that the solutions depend L1-continuously upon their data. The main novelty of the present paper is the presence of two inflection points in the constitutive equation. The Riemann solver constructed here is relevant for fluids in which viscosity and capillarity effects are kept in balance.en_US
dc.formatText
dc.format.extent19 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, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectCompressible fluid dynamicsen_US
dc.subjectPhase transitionsen_US
dc.subjectVan der Waalsen_US
dc.subjectEntropy inequalityen_US
dc.subjectHyperbolic conservation lawen_US
dc.subjectKinetic relationen_US
dc.subjectNonclassical solutionsen_US
dc.subjectRiemann solveren_US
dc.titleNonclassical Riemann Solvers and Kinetic Relations III: A Nonconvex Hyperbolic Model for Van der Waals Fluidsen_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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