Inverse problem of determining the absorption coefficient in a degenerate parabolic equation of divergent type with one spatial variable
https://doi.org/10.26583/vestnik.2025.6.6
EDN: NKNKSM
Abstract
We study the nonlinear inverse problem of determining the unknown time-dependent absorption coefficient in a one-dimensional parabolic equation with a weakly degenerate principal part defined in divergence form. The additional observation condition is specified in integral form. Physically, this means, for example, measuring temperature with a finite-size sensor installed at an interior point of the domain. The solution is understood in a generalized sense; in particular, the unknown absorption coefficient is sought in the space L2(0, T). The equation’s coefficients can depend on both the time and space variables. Degeneracy of the equation is also allowed with respect to both time and space variables. The set of points of degeneracy may be infinite, but must have measure zero. The existence and uniqueness theorems for the solution are proved. The existence of the solution is proven for small T, while the uniqueness theorem is global in nature. Proving the existence of a solution to the inverse problem the latter is reduced to studying the solvability of a certain operator equation, and it is shown that under the conditions imposed in the paper, the operator is contractive
Supporting agencies: The work was carried out with the support of the Priority-2030 Program of NRNU MEPhI
About the Authors
V. L. Kamynin
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
O. V. Nagornov
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
References
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Review
For citations:
Kamynin V.L., Nagornov O.V. Inverse problem of determining the absorption coefficient in a degenerate parabolic equation of divergent type with one spatial variable. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(6):516-524. (In Russ.) https://doi.org/10.26583/vestnik.2025.6.6. EDN: NKNKSM
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