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Matematicheskie Zametki, 2020, Volume 108, Issue 1, Pages 81–93
DOI: https://doi.org/10.4213/mzm12492 (Mi mzm12492) 		 
Approximation of a Multivalued Solution of the Hamilton–Jacobi Equation

E. A. Kolpakovaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.4213/mzm12492
Abstract: The paper deals with the construction of a multivalued solution of the Cauchy problem for the Hamilton–Jacobi equation with discontinuous Hamiltonian with respect to the phase variable. The constructed multivalued solution is approximated by a sequence of continuous solutions of auxiliary Cauchy problems of the Hamilton–Jacobi equation with Hamiltonian which is Lipschitz with respect to the phase variable. The results of the study are illustrated by an example.
Keywords: Hamilton–Jacobi equation, multivalued solution, minimax/viscosity solution, viable set.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 02.A03.21.0006
This work was supported by the Government of the Russian Federation (grant no. 211, contract no. 02.A03.21.0006).
Received: 25.06.2019
Revised: 11.12.2019
English version:
Mathematical Notes, 2020, Volume 108, Issue 1, Pages 77–86
DOI: https://doi.org/10.1134/S000143462007007X
Bibliographic databases:
Document Type: Article
UDC: 517.951
Language: Russian
Citation: E. A. Kolpakova, “Approximation of a Multivalued Solution of the Hamilton–Jacobi Equation”, Mat. Zametki, 108:1 (2020), 81–93; Math. Notes, 108:1 (2020), 77–86
Citation in format AMSBIB
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