Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/hal-00800146
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 13, 2013 - 11:37:04 AM
Last modification on : Sunday, March 29, 2020 - 6:22:03 PM

Links full text

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

373