# Semigeodesics and the minimal time function

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

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

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topNour, 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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