On the solvability of an inverse problem for the Burgers equation with an integral overdetermination condition in a nonlinearly degenerating domain

The paper considers an inverse problem and a direct problem for the Burgers equation in a domain with movable boundaries. With the help of an additional condition, a formula is obtained for determining the desired function from a direct problem for the loaded Burgers equation for the solvability of which we require a condition on the functions according to which the boundaries of the domain change. The solvability of direct problems is proved using a priori estimates and the methods of Faedo-Galerkin and functional analysis.