On the well-posedness of the prediction-control problem for certain systems of equations (Q1033944)

The present paper is devoted to the study of the prediction-observation problem within the framework of an abstract problem for some systems of partial differential equations not resolved for the derivative with respect to time. In particular, the authors investigate inverse problems for a linearized system of Navier-Stokes equations with some overdetermination condition of integral type as well as for a linearized system of equations of the phase field. The authors obtain conditions for the well-defined solvability of these systems. For this purpose they apply many tools from functional analysis, especially from operator theory.