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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2015, Issue 2(46), Pages 193–201 (Mi iimi320)  
The construction of a continuous generalized solution for the Hamilton–Jacobi equations with state constraints

N. N. Subbotinaab, L. G. Shagalovaa

a Institute of Mathematics and Mechanics named after N.N. Krasovskii, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Institute of Mathematics and Computer Science, Ural Federal University named after the first President of Russia B. N. Yeltsin, pr. Lenina, 51, Yekaterinburg, 620083, Russia
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Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00168
Ural Branch of the Russian Academy of Sciences 14-1-НП-348
Received: 05.10.2015
Bibliographic databases:
Document Type: Article
UDC: 517.952, 517.97
MSC: 35D40, 35F21, 9L25
Language: Russian
Citation: N. N. Subbotina, L. G. Shagalova, “The construction of a continuous generalized solution for the Hamilton–Jacobi equations with state constraints”, Izv. IMI UdGU, 2015, no. 2(46), 193–201
Citation in format AMSBIB
\Bibitem{SubSha15}
\by N.~N.~Subbotina, L.~G.~Shagalova
\paper The construction of a continuous generalized solution for the Hamilton--Jacobi equations with state constraints
\jour Izv. IMI UdGU
\yr 2015
\issue 2(46)
\pages 193--201
\mathnet{http://mi.mathnet.ru/iimi320}
\elib{https://elibrary.ru/item.asp?id=25030046}
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