article · Axioms
In this paper, we study the data completion problem for the Cauchy–Stokes equation in a cylindrical domain, Ω. Neumann and Dirichlet boundary conditions are prescribed on part of the overdetermined boundary, Γ0, and the goal is to complete the data on the other part of the boundary, Γa. Here, Γ0 and Γa represent the side faces of the cylinder Ω. This problem is known to be ill-posed and is formulated as an optimal control problem with a regularized cost function. To directly approximate the missing data on Γa, we employ the method of factorization of elliptic boundary value problems. This technique allows the factorization of a boundary value problem into a product of parabolic problems. It is successfully applied to the optimality system in this work, yielding new and significant results.
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DOI: 10.3390/axioms14030177
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