Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
S. K. Godunov, “Interesting class of quasilinear systems,” Dokl. Akad. Nauk SSSR,139, No. 3, 521–423 (1961).
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics [in Russian], Moscow (1968).
V. F. D'yachenko, “On uniqueness conditions for the continuous solution of the problem of decay of a discontinuity for a system of three equations,” Dokl. Akad. Nauk SSSR,153, No. 6, 1245–1248 (1963).
V. A. Tupchiev, “On isolation of the solution of the problem of decay of an arbitrary discontinuity,” Information Bulletin, Numerical Methods of the Mechanics of a Continuous Medium,1, No. 2, 82–95 (1970).
L. P. Eisenhart, Riemannian Geometry, Princeton University Press (1950).
Additional information
Translated from Matematicheskie Zametki, Vol. 13, No. 2, pp. 251–258, February, 1973.
Rights and permissions
About this article
Cite this article
Tupchiev, V.A. On the uniqueness of a continuous solution of the problem of decay of an arbitrary discontinuity for a gradient system. Mathematical Notes of the Academy of Sciences of the USSR 13, 152–157 (1973). https://doi.org/10.1007/BF01094234
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01094234