Geodesic
On the Inverse Problem of Determining the Leading Coefficient in Parabolic Equations
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 48-58

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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.
Mots-clés : parabolic equation
Keywords: inverse problem for the parabolic equation, Poincaré–Steklov inequality, Schauder fixed-point theorem, maximum principle, compact operator. 
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     author = {V. L. Kamynin},
     title = {On the {Inverse} {Problem} of {Determining} the {Leading} {Coefficient} in {Parabolic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {84},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a3/}
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V. L. Kamynin. On the Inverse Problem of Determining the Leading Coefficient in Parabolic Equations. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 48-58. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a3/