On the uniqueness of a continuous solution of the problem of decay of an arbitrary discontinuity for a gradient system

S. K. Godunov has established that the Lagrange variational equations, the differential equations of crystal optics, belong to a class of gradient systems. The problem of the decay of an arbitrary discontinuity for this system is considered herein, and an example is constructed of the ambiguity of a continuous solution of this problem. Moreover, some sufficient conditions for uniqueness of the continuous solution are indicated.