On the determination of an unknown boundary function in a parabolic equation
- 1 January 1999
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 15 (3), 659-667
- https://doi.org/10.1088/0266-5611/15/3/302
Abstract
We study the determination of an unknown boundary function in an initial-boundary value problem for the heat equation. We prove two uniqueness results. In the first one we consider the case of all measurements on a part of the lateral boundary. The second result concerns the case of a single overdetermined datum. Our tools are differentiation with respect to the boundary data and monotonicity estimates that we derive from the maximum principle.Keywords
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