Abstract
Analyzing the controllability problem for the Navier–Stokes equations of a compressible medium requires Carleman estimates of a corresponding adjoint system. The paper presents a Carleman estimate of solutions to two 2D equations, which are adjoint to continuity and momentum equations in compressible-solid mechanics at the start time. The paper proposes a method for generating Carleman estimates for a hyperbolic-parabolic system with Dirichlet and Neumann conditions featuring the same weight function.
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