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- W2164264153 abstract "We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative $L^infty$-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous justification for modeling a small thermal capacity by setting it to zero. We also characterize weak directional derivatives of the temperature with respect to capacity as solutions of related parabolic-elliptic problems." @default.
- W2164264153 created "2016-06-24" @default.
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- W2164264153 date "2007-08-02" @default.
- W2164264153 modified "2023-09-27" @default.
- W2164264153 title "Sensitivity analysis of a parabolic-elliptic problem" @default.
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- W2164264153 doi "https://doi.org/10.1090/s0033-569x-07-01072-4" @default.
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