A source reconstruction algorithm for the Stokes system from incomplete velocity measurements. (7th September 2017) - García, Galina C; Montoya, Cristhian; Osses, Axel
Abstract: We consider the inverse problem of determining the spatial dependence of a source of the form f ( x ) σ ( t ) in the Stokes system defined in Ω × ( 0, T ), assuming that σ ( t ) is known and f ( x ) is divergence-free. The only available observation is a single internal measurement of the velocity and the acceleration, for which one of its components is missing. Under adequate hypothesis on σ we prove uniqueness of this inverse problem and we establish an explicit reconstruction formula. This formula provides the spectral coefficients f k of the source f in terms of a family of null controls h ( τ ) for the corresponding adjoint system indexed by τ ∈ ( 0, T ] .