This paper considers the n-dimensional eikonal equation, which describes the propagation of light in a homogeneous medium from a source on the boundary of a compact set into an unbounded region of n-dimensional space. It is shown that the solution to this problem, obtained using the method of characteristics, can be represented analytically using a formula generalizing Kruzhkov’s formula and is the entropy and minimax solution of the Dirichlet problem in the unbounded region.
Keywords: eikonal equation, homogeneous medium, unbounded region, method of characteristics, superdifferential
Received April 20, 2026
Revised May 05, 2026
Accepted May 12, 2026
Nina Nikolaevna Subbotina, Dr. Phys.-Math. Sci., Corresponding Member of RAS, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620077 Russia; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: subb@uran.ru
Dmitriy Vladimirovich Shemyakin, student, Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: shemdy20@mail.ru
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Cite this article as: N.N. Subbotina, D.V. Shemyakin. Method of characteristics in solving the Dirichlet problem for the eikonal equation in an unbounded domain.Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 2, pp. 231–241.
