Semigeodesics and the minimal time function

Chadi Nour

ESAIM: Control, Optimisation and Calculus of Variations (2005)

  • Volume: 12, Issue: 1, page 120-138
  • ISSN: 1292-8119

Abstract

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We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.

How to cite

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Nour, Chadi. "Semigeodesics and the minimal time function." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2005): 120-138. <http://eudml.org/doc/90784>.

@article{Nour2005,
abstract = { We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations. },
author = {Nour, Chadi},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Minimal time function; Hamilton-Jacobi equations; viscosity solutions; minimal trajectories; eikonal equations; monotonicity of trajectories; proximal analysis; nonsmooth analysis.; Hamilton–Jacobi equation; proximal solution; time-optimal control; differential inclusion},
language = {eng},
month = {12},
number = {1},
pages = {120-138},
publisher = {EDP Sciences},
title = {Semigeodesics and the minimal time function},
url = {http://eudml.org/doc/90784},
volume = {12},
year = {2005},
}

TY - JOUR
AU - Nour, Chadi
TI - Semigeodesics and the minimal time function
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2005/12//
PB - EDP Sciences
VL - 12
IS - 1
SP - 120
EP - 138
AB - We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.
LA - eng
KW - Minimal time function; Hamilton-Jacobi equations; viscosity solutions; minimal trajectories; eikonal equations; monotonicity of trajectories; proximal analysis; nonsmooth analysis.; Hamilton–Jacobi equation; proximal solution; time-optimal control; differential inclusion
UR - http://eudml.org/doc/90784
ER -

References

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