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- Title
On the inverse problem of determining the leading coefficient in parabolic equations.
- Authors
Kamynin, V. L.
- Abstract
We study the unique solvability of the inverse problem of determining the leading coefficient in the parabolic equation on the plane with coefficients depending on both time and spatial variables under the condition of integral overdetermination with respect to time. We obtain sufficient conditions for the unique solvability of the inverse problem. We present nontrivial examples of problems for which such conditions hold. It is shown that the imposed conditions necessarily hold if either the time interval is sufficiently large or the space interval on which the problem is considered is sufficiently small.
- Subjects
HYPERSPACE; DIFFERENTIAL geometry; PARABOLIC differential equations; INVERSE problems; DIFFERENTIAL equations; SPACETIME; MATHEMATICAL analysis
- Publication
Mathematical Notes, 2008, Vol 84, Issue 1-2, p45
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434608070043