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Constraining inverse Stefan design problems. (English) Zbl 0864.76089
A new formulation possessing stable numerical characteristics is presented for inverse Stefan design processes. In such processes, the goal is to design transient boundary conditions which produce the desired interfacial surface motion. This subclass of mildly ill-posed mathematical problems is amenable to the proposed solution methodology. This investigation presents a fixed-front differential formulation from which a weighted residual statement is developed. Orthogonal collocation is used to obtain numerical results illustrating the merit of imposing physical constraints in the mathematical model.

MSC:
76T99 Multiphase and multicomponent flows
80A22 Stefan problems, phase changes, etc.
35R30 Inverse problems for PDEs
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