Inverse problems of recovering parameters in the Lin–Reissner–Tsien equation

The article is devoted to the study of the solvability of new nonlinear inverse problems of finding an unknown constant together with solving the linearized Lin–Reissner–Tsien equation. For the problems under consideration, theorems of solvability are proved in classes of regular solutions, i.e., of solutions having all weak derivatives in the sense of S.L. Sobolev that occur in the corresponding equation.
The peculiarity of the problems under study is, firstly, that the unknown coefficient is a constant (which corresponds, for example, to a homogeneous medium). Secondly, a new overdetermination condition, not previously used by the predecessors, is introduced: an integral condition with respect to the time variable.