Geodesic
The construction of a continuous generalized solution for the Hamilton--Jacobi equations with state constraints
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 193-201

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We consider a boundary value problem with state constraints for a nonlinear non-coercive Hamilton–Jacobi equation. We introduce a new definition of continuous generalized solution of the problem and apply this definition to nonlinear non-coercive equation arising in molecular biology. The construction for generalized solution with additional requirements to structure is provided for this equation. Connections with viscosity generalized solutions are discussed. Results of computer simulations are exposed.
Keywords: Hamilton–Jacobi equation, generalized solution, viscosity solution, minimax solution, state constraints, method of characteristics. 
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     author = {N. N. Subbotina and L. G. Shagalova},
     title = {The construction of a continuous generalized solution for the {Hamilton--Jacobi} equations with state constraints},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a24/}
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N. N. Subbotina; L. G. Shagalova. The construction of a continuous generalized solution for the Hamilton--Jacobi equations with state constraints. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 193-201. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a24/