Geodesic
Method of characteristics for optimal control problems and conservation laws
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 204-210

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In this paper, notions of global generalized solutions of Cauchy problems for the Hamilton–Jacobi–Bellman equation and for a quasilinear equation (a conservation law) are introduced in terms of characteristics of the Hamilton–Jacobi equation. Theorems on the existence and uniqueness of generalized solutions are proved. Representative formulas for generalized solutions are obtained and a relation between generalized solutions of the mentioned problems is justified. These results tie nonlinear scalar optimal control problems and one-dimensional stationary conservation laws. 
@article{CMFD_2011_42_a19,
     author = {N. N. Subbotina and E. A. Kolpakova},
     title = {Method of characteristics for optimal control problems and conservation laws},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {204--210},
     publisher = {mathdoc},
     volume = {42},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2011_42_a19/}
}
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N. N. Subbotina; E. A. Kolpakova. Method of characteristics for optimal control problems and conservation laws. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 204-210. http://geodesic.mathdoc.fr/item/CMFD_2011_42_a19/