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Lyapunov functions for infinite-dimensional systems. (English) Zbl 1040.93062

Summary: We study Lyapunov functions for infinite-dimensional dynamical systems governed by general maximal monotone operators. We obtain a characterization of Lyapunov pairs by means of the associated Hamilton-Jacobi partial differential equations, whose solutions are meant in the viscosity sense, as evolved in works of Tataru and Crandall-Lions. Our approach also leads to a new sufficient condition for Lyapunov pairs, generalizing a classical result of Pazy.

MSC:

93D30 Lyapunov and storage functions
93C25 Control/observation systems in abstract spaces
93B28 Operator-theoretic methods
49L20 Dynamic programming in optimal control and differential games
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