Geodesic
Approximation of a Multivalued Solution of the Hamilton--Jacobi Equation
Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 81-93

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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. 
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     author = {E. A. Kolpakova},
     title = {Approximation of a {Multivalued} {Solution} of the {Hamilton--Jacobi} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {81--93},
     publisher = {mathdoc},
     volume = {108},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a5/}
}
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E. A. Kolpakova. Approximation of a Multivalued Solution of the Hamilton--Jacobi Equation. Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 81-93. http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a5/