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Articles 1 - 2 of 2
Full-Text Articles in Applied Mathematics
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
On The Inverse Multiphase Stefan Problem, Bruno Giuseppe Poggi Cevallos
Theses and Dissertations
We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary heat flux is the control, and optimality criteria consists of the minimization of the L₂-norm declination of the trace of the solution to the Stefan problem from the temperature measurement on the fixed boundary. State vector solves multiphase Stefan problem in a weak formulation, which is equivalent to Neumann problem for the quasilinear parabolic PDE with discontinuous coefficient. Full discretization through finite differences is …
Random Walks On Random Lattices And Their Applications, Ryan Tyler White
Random Walks On Random Lattices And Their Applications, Ryan Tyler White
Theses and Dissertations
This work studies a class of continuous-time, multidimensional random walk processes with mutually dependent random step sizes and their exits from hyperrectangles. Fluctuations of the process about the critical boundary are studied extensively by stochastic analysis and operational calculus. Further, information on the process can be ascertained only upon observations occurring according to a delayed renewal process, rather than in real time. Passage times are thus obscured and results are first derived pertaining to the pre-passage and post-passage observations. Two distinct strategies are developed to combat the crudeness of delayed observations in order to derive more refined information about the …