Graduate Thesis Or Dissertation
 

Nonlinear free boundary problems arising from melting processes

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  • We discuss a mathematical model arising in the melting of a fluid in two spatial dimensions and in time. The model leads to a free boundary value problem for determining the location of the interface as well as the temperature distribution. The movement of the interface depends on the temperatures, the velocities and the material properties at the interface through conditions of dynamical compatibility for energy transfer. In this study, we assume that the density and pressure are constant. A numerical approximation making use of finite differences and the maximum principle is used to present existence and uniqueness theorems and continuous dependence of the solution on the data. Finally, numerical algorithms for finding approximate solutions and the results of numerical calculations are given.
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  • Master files scanned at 600 ppi (256 Grayscale) using Capture Perfect 3.0.82 on a Canon DR-9080C in TIF format. PDF derivative scanned at 300 ppi (256 B&W), using Capture Perfect 3.0.82, on a Canon DR-9080C. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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