Geodesic
On constructions of the generalized solution of the Hamilton--Jacobi equation in bounded domains
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 126-127

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The Cauchy problem with state constraints for the Hamilton–Jacobi equation arising in molecular biology is considered. The notion of a continuous generalized solution to the problem is introduced. Conditions are given to construct the continuous solution in bounded domains with the help of characteristics started from the initial manifold.
Keywords: Hamilton–Jacobi equations, method of characteristics, generalized solutions. 
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     title = {On constructions of the generalized solution of the {Hamilton--Jacobi} equation in bounded domains},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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N. N. Subbotina; L. G. Shagalova. On constructions of the generalized solution of the Hamilton--Jacobi equation in bounded domains. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 39 (2012) no. 1, pp. 126-127. http://geodesic.mathdoc.fr/item/IIMI_2012_39_1_a60/