On solvability of some inverse problems for a nonlocal fourth-order parabolic equation with multiple involution
Turmetov B. Karachik V.
2024American Institute of Mathematical Sciences
AIMS Mathematics
2024#9Issue 36832 - 6849 pp.
In this paper, the solvability of some inverse problems for a nonlocal analogue of a fourth-order parabolic equation was studied. For this purpose, a nonlocal analogue of the biharmonic operator was introduced. When defining this operator, transformations of the involution type were used. In a parallelepiped, the eigenfunctions and eigenvalues of the Dirichlet type problem for a nonlocal biharmonic operator were studied. The eigenfunctions and eigenvalues for this problem were constructed explicitly and the completeness of the system of eigenfunctions was proved. Two types of inverse problems on finding a solution to the equation and its righthand side were studied. In the two problems, both of the righthand terms depending on the spatial variable and the temporal variable were obtained by using the Fourier variable separation method or reducing it to an integral equation. The theorems for the existence and uniqueness of the solution were proved.
eigenfunction , eigenvalue , existence of solution , Fourier method , inverse problem , nonlocal biharmonic operator , parabolic equation , uniqueness of solution
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Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, Kazakhstan
Department of Mathematical Analysis, South Ural State University, Chelyabinsk, Russian Federation
Department of Mathematics
Department of Mathematical Analysis
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