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In this paper, an initial boundary value problem for nonlinear Klein‐Gordon equation is considered. Giving an additional condition, a time‐dependent coefficient multiplying nonlinear term is determined, and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem.

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In this paper, the inverse problem of finding a coefficient in a second order elliptic equation is investigated. The conditions for the existence and uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.

In the paper an inverse boundary value problem for the Boussinesq-Love equation with the integral condition of the first kind is investigated. First given problem is reduced to the equivalent problem in a known sense. Then, using the method of Fourier equivalent problem is reduced to the solution of the system of integral equations. Further, the existence and uniqueness of the integral equation is proved by means of the contraction mappings principle, which is also the unique solution of the equivalent problem. Finally, using the equivalence, the theorem on the existence and uniqueness of a classical solution of the given problem is proved.