| Abstract: |
| This work investigated the solvability of a some inverse issues for a high-order parabolic equations nonlocal analogue. Non local equivalent of the biharmonic operator has been developed for this purpose. Transformations of the involution type were used in the definition of this operator. The eigenfunctions and eigenvalues of the Dirichlet type problem for a nonlocal biharmonic operator have been studied in a parallelepiped. For this particular problem, the eigenvalues and eigenfunctions were explicitly constructed, and the proof of the system`s completeness was presented. We examined two different kinds of inverse problems that involved solving the equation and its right-hand side. Using the Fourier variable separation approach or reducing it to an integral equation, the two problems` right hand terms that depended on the spatial and temporal variables were found. The theorems for the existence and uniqueness of the solution were proved. |
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