Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations

Abstract : We state and prove a "Lax-Hopf formula" characterizing viable capture basins of targets investigated in viability theory and derive a "Max-Plus" morphism of capture basins with respect to the target. Capture basins are used to define "viability solutions" to Hamilton-Jacobi equations satisfying "trajectory conditions" (initial, boundary or Lagrangian conditions). The Max-Plus morphism property of Lax-Hopf formula implies the fact that the solution associated with inf-convolution of trajectory conditions is the inf-convolution of the solutions for each trajectory condition. For instance, Lipschitz regularization or decreasing envelopes of trajectory condition imply the Lipschitz regulation or decreasing envelopes of the solutions.
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Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20 (2), pp.187-211. 〈10.1007/s00030-012-0188-8〉
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Contributeur : Estelle Bouzat <>
Soumis le : mercredi 13 mars 2013 - 11:37:04
Dernière modification le : jeudi 10 mai 2018 - 02:00:54

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Jean-Pierre Aubin. Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations. Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20 (2), pp.187-211. 〈10.1007/s00030-012-0188-8〉. 〈hal-00800146〉

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