Generalized Solutions of Hamilton – Jacobi Equation to a Molecular Genetic Model

Abstract : A boundary value problem with state constraints is under consideration for a nonlinear noncoercive Hamilton-Jacobi equation. The problem arises in molecular biology for the Crow – Kimura model of genetic evolution. A new notion of continuous generalized solution to the problem is suggested. Connections with viscosity and minimax generalized solutions are discussed. In this paper the problem is studied for the case of additional requirements to structure of solutions. Constructions of the solutions with prescribed properties are provided and justified via dynamic programming and calculus of variations. Results of simulations are exposed.
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Nina Subbotina, Lyubov Shagalova. Generalized Solutions of Hamilton – Jacobi Equation to a Molecular Genetic Model. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.462-471, ⟨10.1007/978-3-319-55795-3_44⟩. ⟨hal-01626917⟩

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