Geodesic
Construction of a~continuous minimax/viscosity solution of the Hamilton--Jacobi--Bellman equation with nonextendable characteristics
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 247-257

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The Cauchy problem for the Hamilton–Jacobi equation, which appears in molecular biology for the Crow–Kimura model of molecular evolution, is considered. The state characteristics of the equation that start in a given initial manifold bounded in the state space stay in a strip bounded in the state variable and fill a part of this strip. The values attained by the impulse characteristics on a finite time interval are arbitrarily large in magnitude. We propose a construction of a smooth extension for a continuous minimax/viscosity solution of the problem to the part of the strip that is not covered by the characteristics starting in the initial manifold.
Keywords: Hamilton–Jacobi–Bellman equations, method of characteristics, viscosity solutions, minimax solutions. 
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     author = {N. N. Subbotina and L. G. Shagalova},
     title = {Construction of a~continuous minimax/viscosity solution of the {Hamilton--Jacobi--Bellman} equation with nonextendable characteristics},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {247--257},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a21/}
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N. N. Subbotina; L. G. Shagalova. Construction of a~continuous minimax/viscosity solution of the Hamilton--Jacobi--Bellman equation with nonextendable characteristics. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 247-257. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a21/