Abstract
The paper considers a loaded wave equation. Its peculiarity is that in characteristic variables $\xi=x-y$, $\eta=x+y$, the loaded components are a linear combination of unknown functions, which depend only on $\xi$ or $\eta$. Moreover, the loaded part of this equation is a solution to the wave equation. For such an equation a representation of all its solutions is obtained. The problem is investigated in the case where the carrier is one of the characteristics of the wave equation, a setting known to be ill-posed for the usual string oscillation equation. For the Cauchy problem, the same characteristic carrier is considered. For a normal wave equation, such a formulation is known to be ill-posed. When some nonlocal conditions of a point nature are satisfied, the existence and uniqueness theorem for the given problem is proved, and the solution is written out explicitly. This shows the effect of the load as a regulator of the ill-posed problem.