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Lyapunov Functions for Infinite-Dimensional Systems
Authors:Maciej Kocan  Pierpaolo Soravia
Institution:
  • a Mathematics Institute, University of Cologne, Cologne, 50923, Germany, 22Also, Centre for Mathematics and its Applications, Australian National University, Canberra.
  • b Dipartimento di Matematica Pura e Applicata, via Belzoni 7, Padova, 35131, Italyf1soravia@math.unipd.itf1
  • Abstract: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.
    Keywords:viscosity solutions  nonlinear semigroups  accretive operators  optimality principles  stability  Lyapunov functionals  Lyapunov method  
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