Geodesic
An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 180-191

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In this paper we investigate an identification problem of a coefficient at the nonlinear lowest term in a 2D semilinear parabolic equation with overdetermination conditions given on a smooth curve. The unknown coefficient has the form of a product of two functions each depending on time and a spatial variable. We prove solvability of the problem in classes of smooth bounded functions. We present an example of input data satisfying the conditions of the theorem and the corresponding solution.
Keywords: inverse problem, semilinear parabolic equation, Cauchy problem, lowest term coefficient, weak approximation method, local solvability, overdetermination conditions on a smooth curve. 
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     author = {Ekaterina N. Kriger and Igor V. Frolenkov},
     title = {An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     number = {2},
     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a6/}
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Ekaterina N. Kriger; Igor V. Frolenkov. An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 180-191. http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a6/