Abstract
The work is devoted to the study of the solvability of new inverse problems of determining, together with the solution of parabolic or hyperbolic equations, a certain coefficient of the equation itself. A feature of the problems under study is, firstly, that the unknown coefficient is sought in the class of constant functions and, secondly, that a new, previously unused redefinition condition is applied. For the problems under study, existence theorems are proved for regular solutions, which are the solutions having all the derivatives generalized in the Sobolev sense entering the corresponding equation.
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