FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2189368509> ?p ?o ?g. }

• W2189368509 abstract " Abstract—This paper is devoted to the two-phase Stefan problem with the irregular diving boundary of the region. We consider a two-dimensional heat equation with two known boundary conditions in one at the left-hand-side and the other at the right-hand-side. We construct the Green's function in a dihedral angle for the heat equation with the coupled conditions on the fixed known boundary of division two- phases. Then, using this defined Green's function and its properties, we obtain integral representatives of the temperature distributions and the low of motion of the diving boundary. Uniqueness and regularity of the constructed analytic solution with the diving boundary have been proved in the weighted Sobolev space. Index Terms—Green's function with irregular boundary, two-phase Stefan problem, motion of the diving boundary I. INTRODUCTION he two-phase Stefan problem consists of determining a temperature field and the low of motion of the diving boundary separating the two phases. It describes a solidification process involving various physical phenomena, including conduction with phase change which is characterized by a moving interface separating two phases and the two-phase heat and mass transfer process. We will start with solving the heat equation, which governs the temperature distribution in the liquid and the solid phases. The unknowns are the two temperature distributions and the position of an interface between the phases (free boundary). The description of the moving interface problem includes the heat transfer equations for each phase with corresponding initial and boundary conditions which should be specified in each phase as well as on the interface. We have considered the weak formulation of the two-phase Stefan problem and presented the analytical method of solution in the dihedral angle. The classical solutions of the two dimensional two-phase Stefan problem are not expected to exist for all domains (1). An investigation of the coupled problems for the heat conduction equation with irregular boundary showed that the Stefan problem can't be solved in the functional space with a regular metric in the dihedral angle. This fact motivates the study of the weak solutions in the weighted Sobolev space. For the numerical solution of the Stefan problem traditionally are used Galerkin methods which combined with suitable explicit Runge-Kutta time stepping schemes or the implicit Euler method for the temporal discretization. Linearized formulation of the Stefan problem is possible, if we consider the problem in a small interval of time t ∈ (0; T), assuming that the unknown boundary changes during this time slightly. The mathematical theory of the local solvability for the one-phase Stefan problem for the one-dimensional heat equation on a small time interval was considered by A.M.Meirmanov (1), E.I.Hanzava (2), B.V.Basalii (4), E.V. Radcevich (5). The existence theorem for a parabolic equation in a small time period was proven by A.M.Meirmanov. The solution was obtained by using the auxiliary regularized tasks. The obtained estimates for the solutions of the auxiliary problems allowed one to get the compactness of the solution in the space ) 1 , 2 ( C. The Green's function in the dihedral angle for the heat equation was built in the Holder space by V.A Solonnikov and E.V.Frolovova (3). These results are used to prove the solvability of boundary value problems for the heat equation in a dihedral angle. The objective of this paper is to develop a similar theory and construct an analytical solution for the two-phase Stefan problem in the dihedral angle. The construction of the analytical solution for the two-dimensional two-phase Stefan problem will be based on the Green's function for the temperature distribution in the two phases in a domain with a fixed boundary. The properties and features of the constructed Green's function are essentially provided existence and uniqueness of the temperature field and the law of motion of the dividing boundary for the two- dimensional two-phase Stefan problem. This result gives some general properties and features for the temperature distributions and the law of motion of the irregular dividing boundary." @default.
• W2189368509 created "2016-06-24" @default.
• W2189368509 creator A5039579137 @default.
• W2189368509 date "2013-01-01" @default.
• W2189368509 modified "2023-09-27" @default.
• W2189368509 title "The Two-phase Stefan Problem for the Heat Equation" @default.
• W2189368509 cites W2004219338 @default.
• W2189368509 cites W2046962879 @default.
• W2189368509 cites W2145809352 @default.
• W2189368509 cites W2157005274 @default.
• W2189368509 cites W604181985 @default.
• W2189368509 hasPublicationYear "2013" @default.
• W2189368509 type Work @default.
• W2189368509 sameAs 2189368509 @default.
• W2189368509 citedByCount "0" @default.
• W2189368509 crossrefType "journal-article" @default.
• W2189368509 hasAuthorship W2189368509A5039579137 @default.
• W2189368509 hasConcept C121332964 @default.
• W2189368509 hasConcept C134306372 @default.
• W2189368509 hasConcept C154416045 @default.
• W2189368509 hasConcept C182310444 @default.
• W2189368509 hasConcept C202787564 @default.
• W2189368509 hasConcept C2778021227 @default.
• W2189368509 hasConcept C33923547 @default.
• W2189368509 hasConcept C44280652 @default.
• W2189368509 hasConcept C50517652 @default.
• W2189368509 hasConcept C57879066 @default.
• W2189368509 hasConcept C62354387 @default.
• W2189368509 hasConcept C62520636 @default.
• W2189368509 hasConceptScore W2189368509C121332964 @default.
• W2189368509 hasConceptScore W2189368509C134306372 @default.
• W2189368509 hasConceptScore W2189368509C154416045 @default.
• W2189368509 hasConceptScore W2189368509C182310444 @default.
• W2189368509 hasConceptScore W2189368509C202787564 @default.
• W2189368509 hasConceptScore W2189368509C2778021227 @default.
• W2189368509 hasConceptScore W2189368509C33923547 @default.
• W2189368509 hasConceptScore W2189368509C44280652 @default.
• W2189368509 hasConceptScore W2189368509C50517652 @default.
• W2189368509 hasConceptScore W2189368509C57879066 @default.
• W2189368509 hasConceptScore W2189368509C62354387 @default.
• W2189368509 hasConceptScore W2189368509C62520636 @default.
• W2189368509 hasLocation W21893685091 @default.
• W2189368509 hasOpenAccess W2189368509 @default.
• W2189368509 hasPrimaryLocation W21893685091 @default.
• W2189368509 hasRelatedWork W1999264981 @default.
• W2189368509 hasRelatedWork W2015898652 @default.
• W2189368509 hasRelatedWork W2020280307 @default.
• W2189368509 hasRelatedWork W2020571742 @default.
• W2189368509 hasRelatedWork W2050323259 @default.
• W2189368509 hasRelatedWork W2066577036 @default.
• W2189368509 hasRelatedWork W2090852104 @default.
• W2189368509 hasRelatedWork W2104305375 @default.
• W2189368509 hasRelatedWork W2157616447 @default.
• W2189368509 hasRelatedWork W2165825358 @default.
• W2189368509 hasRelatedWork W2539340507 @default.
• W2189368509 hasRelatedWork W2893737545 @default.
• W2189368509 hasRelatedWork W2896762735 @default.
• W2189368509 hasRelatedWork W2950034567 @default.
• W2189368509 hasRelatedWork W2952379579 @default.
• W2189368509 hasRelatedWork W3082974596 @default.
• W2189368509 hasRelatedWork W3083395091 @default.
• W2189368509 hasRelatedWork W342313240 @default.
• W2189368509 hasRelatedWork W43096700 @default.
• W2189368509 hasRelatedWork W2189523157 @default.
• W2189368509 isParatext "false" @default.
• W2189368509 isRetracted "false" @default.
• W2189368509 magId "2189368509" @default.
• W2189368509 workType "article" @default.