Abstract
In the paper, parabolic-elliptic problems with time-dependent obstacles and variable boundary conditions are considered. The obstacles are either concentrated at a given time-dependent part of the boundary of a geometric domain or within a prescribed time-dependent subdomain. The problems are fourmulated as a Cauchy problem in Hilbert space. Existence and uniqueness results are established, in particular refering to some models of flows in porous media and electrochemical machining processes with moving control actions.
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Kenmochi, N., Pawlow, I. Parabolic-elliptic free boundary problems with time-dependent obstacles. Japan J. Appl. Math. 5, 87–121 (1988). https://doi.org/10.1007/BF03167902
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DOI: https://doi.org/10.1007/BF03167902