Mathematics & Physics 2016, 9(2), 180–191 УДК 517.9 An Identification Problem of Nonlinear Lowest Term Coefficient in the Special Form for Two-Dimensional Semilinear Parabolic Equation Ekaterina N. Kriger∗ Igor V.Frolenkov† Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 10.12.2015, received in revised form 16.02.2016, accepted 18.03.2016 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. <...> We consider an identification problem of a special coefficient at the nonlinear term in a twodimensional semilinear parabolic equation with Cauchy data. <...> By means of overdetermination conditions the given inverse problem is reduced to a nonclassical direct problem for a loaded parabolic equation. <...> Solvability of the direct problem is proved by the weak approximation method [1–3]. <...> Efficiency of the weak approximation method (the splitting method at differential level) is that, as a rule, on every fractional step the split problem is simpler than the original one. <...> For the original inverse problem we prove a theorem of the solution existence in classes of smooth bounded functions. <...> Earlier, the problems of coefficient identification for semilinear parabolic equations with Cauchy data have been studied in papers [4, 5]. <...> In [6] the problem of identification of two coefficients in a semilinear parabolic equation with overdetermination conditions on smooth curves has been considered. <...> Solvability of the identification problem of a coefficient represented as a sum of two functions at a nonlinear term in a semilinear parabolic equation has been investigated in [7]. <...> In paper [8] unique solvability of an inverse boundary-value problem for an one-dimensional semilinear parabolic equation with the sought for coefficient f(t) + g(x) at the lowest term has ∗e_katherina@mail.ru †igor@frolenkov.ru ⃝ Siberian Federal University <...>