Date Received: Feb 18, 2019
Date Published: Mar 18, 2019
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A Stability Estimate for Robin Boundary Coefficients in Stokes Fluid Flows
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Nguyen Thuy Dung
1
Keywords
inverse problems, Carleman inequality, Stokes equation, Stability estimate
Abstract
In this report, we examine the unsteady Stokes equations with non-homogeneous boundary conditions. As an application of a Carleman estimate, we first establish log type stabilities for the solution of the equations from either an interior measurement of the velocity, or a boundary observation depending on the trace of the velocity and of the Cauchy stress tensor measurements on a part of the boundary. We then consider the inverse problem of determining the time-independent Robin coefficient from a measurement of the solution and of Cauchy data on a sub-boundary.
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