Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Nonlinear Differential Equations and Applications Year : 2013

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.

Dates and versions

hal-00800146 , version 1 (13-03-2013)

Identifiers

Cite

Jean-Pierre Aubin. Lax-Hopf formula and Max-Plus properties of solutions to Hamilton-Jacobi equations. Nonlinear Differential Equations and Applications, 2013, 20 (2), pp.187-211. ⟨10.1007/s00030-012-0188-8⟩. ⟨hal-00800146⟩
143 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More