Geodesic
An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 22-37

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In this paper we consider the problem of identification of coefficient at nonlinear lowest term for two-dimensional semilinear parabolic equation. The sought-for coefficient depends on all variables and has the form of the sum of two functions each of them depends on time and on a spatial variable. The indicated inverse problem is reduced to non-classical direct problem which contains the traces of unknown function and its derivatives. The investigation of existence and uniqueness of solution of the auxiliary direct problem is carried out by means of the weak approximation method. We prove theorems of existence and uniqueness of the inverse problem solution in classes of smooth bounded functions. We present an example of input data satisfying the conditions of the proved theorems and corresponding solution.
Keywords: inverse problem, semilinear parabolic equation, weak approximation method, coefficient at lowest term, Cauchy problem, existence and uniqueness of solution. 
@article{IVM_2015_5_a2,
     author = {E. N. Kriger and I. V. Frolenkov},
     title = {An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the {Cauchy} data},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {22--37},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_5_a2/}
}
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E. N. Kriger; I. V. Frolenkov. An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 22-37. http://geodesic.mathdoc.fr/item/IVM_2015_5_a2/