12:00 pm Friday, September 11, 2015
Junior Analysis: On an inverse free boundary problem for a second-order linear parabolic PDE by Nick Crispi in RLM 11.176
Based on the work of U.G. Abdulla, we mathematically investigate the Inverse Stefan Problem (ISP), an inverse free boundary problem for a second-order linear parabolic PDE whose solution, having time and depth as independent variables, represents temperature in a medium undergoing a phase transition. We devise from ISP an optimal control problem that takes the free boundary and the unknown heat flux on the fixed boundary as controls, which, if chosen “optimally,” minimize a prescribed cost functional and give rise to a “best approximate solution.” We prove that this (infinite dimensional) optimal control problem is the limit of more tractable finite dimensional optimal control problems rendered from certain FDM approximations, in the sense that the minimums and minimizers of the cost functionals in the finite dimensional problems respectively approach the minimum and minimizers of the cost functional from infinite dimensional problem (which we must prove exist in the first place). Submitted by
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