Geodesic
Construction of a~generalized solution to an equation that preserves the Bellman type in a~given domain of the state space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 243-256

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A Cauchy problem is considered for a Hamilton–Jacobi equation that preserves the Bellman type in a spatially bounded strip. Sufficient conditions are obtained under which there exists a continuous generalized (minimax/viscosity) solution to this problem with a given structure in the strip. A construction of this solution is presented. 
@article{TM_2012_277_a16,
     author = {N. N. Subbotina and L. G. Shagalova},
     title = {Construction of a~generalized solution to an equation that preserves the {Bellman} type in a~given domain of the state space},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {243--256},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_277_a16/}
}
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N. N. Subbotina; L. G. Shagalova. Construction of a~generalized solution to an equation that preserves the Bellman type in a~given domain of the state space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 243-256. http://geodesic.mathdoc.fr/item/TM_2012_277_a16/