Free interface problems modeling solid combustion and rapid solidification
Abstract
This dissertation is devoted to the study of free interface problem modeling solid combustion and rapid solidification of supercooled pure liquids. The problem possesses a thermal feedback mechanism resulting from the interaction between the interface kinetics and the heat diffusion and generating a variety of nontrivial oscillatory regimes in the interface motion as the basic traveling wave solution looses its stability. Rigorous analysis demonstrates global in time existence of classical solutions, their uniform boundedness and smoothness of the interface motion regardless of the strength and complexity of the oscillations. Similar properties are established for several related problems. Numerical simulation of the problem allows for a comprehensive description of the dynamical scenarios exhibited by the interface motion.
Degree
Ph.D.
Advisors
Frankel, Purdue University.
Subject Area
Mathematics|Mechanical engineering
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