A dynamic inverse problem for a one-dimensional system of the Hopf-type equations is considered. A theorem on local solvability in the class of functions
analytic in the variable *x* is proved.

A one-dimensional system of the Hopf-type equations is considered. Axial solutions to problems in the field of modeling two-fluid interactions are sought. A nonlinear system of ordinary differential equations is obtained. Direct and inverse problems for the obtained ODE are considered. A theorem on local solvability is proven.

In the data assimilation algorithms for the air quality applications, the source identification problem can be considered as an auxiliary one for the solution of the model state function continuation problem. The algorithm based on the ensembles of the adjoint problem solutions is applied to solve the inverse problems. The...

We investigate the continuation problem for the elliptic equation. The continuation problem is formulated in the operator form *Aq = f*. Singular values of the operator *A* are presented and analyzed for the continuation problem for the Helmholtz equation. Results of numerical experiments are presented.