The research of a Stefan problem with unknown pressure in a liquid phase. (October 2020)

• Record Type: Journal Article
• Authors: Tilepiev, Murat; Beisebay, Perizat; Aruova, Aliya; Akzhigitov, Erbulat
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: The melting process -- Heavy paraffin-base crude oil -- A Stefan problem -- Parabolic equations of the second order -- Boundary value problems -- Tasks with free borders; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103124
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider mathematical modeling of problems with free boundaries, namely, the investigation of the Stefan type problem with a non-constant melting point, taking into account the pressure in the liquid phase. A mathematical model has been constructed that describes the melting process of heavy paraffin-base crude oil. We prove an existence and uniqueness of a solution of a Stefan-type problem in the Holder spaces with a melting point that depends on the unknown pressure are considered. We study the solvability in Holder spaces and the asymptotic behavior for t, which tends to ∞, solving a single-phase Stefan-type problem for a nonlinear parabolic equation.