PUBLISHED PAPERS #04.04
| Igor Chernin, Elvin Azizbayov. On an Inverse Problem of Determining the Time Derivative Coefficient in a Parabolic Equation |
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| Abstract. This paper studies a nonlocal inverse boundary-value problem for a second-order parabolic equation. The primary objective is to identify the time derivative coefficient in the parabolic equation using additional measurements. To analyze the classical solvability of the original problem, the considered problem is reduced to an auxiliary inverse boundary-value problem. Furthermore, the existence and uniqueness theorem for the solution to the equivalent problem is proved. Finally, using this equivalence, sufficient conditions for the existence and uniqueness of the classical solution to the inverse problem for the second-order parabolic equation are established. |
| Keywords: inverse problem, parabolic equation, classical solution, existence, uniqueness |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1002 |