Geodesic
On the uniqueness of a~continuous solution of the problem of decay of an~arbitrary discontinuity for a~gradient system
Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 251-258.

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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. 
@article{MZM_1973_13_2_a9,
     author = {V. A. Tupchiev},
     title = {On the uniqueness of a~continuous solution of the problem of decay of an~arbitrary discontinuity for a~gradient system},
     journal = {Matemati\v{c}eskie zametki},
     pages = {251--258},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a9/}
}
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V. A. Tupchiev. On the uniqueness of a~continuous solution of the problem of decay of an~arbitrary discontinuity for a~gradient system. Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 251-258. http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a9/