A source reconstruction algorithm for the Stokes system from incomplete velocity measurements. (7th September 2017)

• Record Type: Journal Article
• Authors: García, Galina C; Montoya, Cristhian; Osses, Axel
• Is Part Of: Inverse problems. Volume 33:Number 10(2017:Oct.)
• Publication Date: 2017-09-07
• Subjects: inverse source problem -- null controllability -- stokes system; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa863f
• Languages: English
• ISSNs: 0266-5611

Abstract

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 ] .