On the existence and uniqueness of the solution of the coefficient inverse problem for a semilinear parabolic equation

Abstract

Abstract In this paper, we consider the problem of determining the source function and the coefficient by the derivative with respect to time in a semilinear parabolic equation with overdetermination conditions defined on two different hyperplanes. The existence and uniqueness theorems of the classical solution of the posed coefficient inverse problem in the class of smooth bounded functions were proved. An example of input data satisfying the conditions of the proved theorems is given.