Abstract
The paper is devoted to the development of the viscosity approach to the generalized solution of functional Hamilton-Jacobi type equations with coinvariant derivatives and a nonanticipatory Hamiltonian. These equations are naturally connected to problems of dynamical optimization of hereditary systems and, as compared with classical Hamilton-Jacobi equations, possess a number of additional peculiarities stipulated by the aftereffect. The definition of a viscosity solution that takes the above peculiarities into account is given. The consistency of this definition with the notion of a classical solution and with the minimax approach to the generalized solution is substantiated. The existence and uniqueness theorems are proved.
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Original Russian Text © N. Yu. Lukoyanov, 2007, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2007, Vol. 13, No. 2.
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Lukoyanov, N.Y. On viscosity solution of functional Hamilton-Jacobi type equations for hereditary systems. Proc. Steklov Inst. Math. 259 (Suppl 2), S190–S200 (2007). https://doi.org/10.1134/S0081543807060132
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DOI: https://doi.org/10.1134/S0081543807060132