Stability of Discontinuous Diffusion Coefficients and Initial Conditions in an Inverse Problem for the Heat Equation
نویسندگان
چکیده
We consider the heat equation with a discontinuous diffusion coefficient and give uniqueness and stability results for both the diffusion coefficient and the initial condition from a measurement of the solution on an arbitrary part of the boundary and at some arbitrary positive time. The key ingredient is the derivation of a Carleman-type estimate. The diffusion coefficient is assumed to be discontinuous across an interface with a monotonicity condition. AMS 2000 subject classification: 35K05, 35R30.
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عنوان ژورنال:
- SIAM J. Control and Optimization
دوره 46 شماره
صفحات -
تاریخ انتشار 2007