We define viscosity solutions for the Hamilton-Jacobi equation φt=v(x,t)H(∇φ) in RN×(0,∞) where v is positive and bounded measurable and H is non-negative and Lipschitz continuous. Under certain assumptions, we establish the existence and uniqueness of Lipschitz continuous viscosity solutions. The uniqueness result holds in particular for those v which are independent of t and piecewise continuous with discontinuous sets consisting of finitely many smooth lower dimensional surfaces not tangent to each other at any point of their intersection.ets are determined by the solution of a disc packing problem.
1
University of Pittsburgh, United States
2
University of Notre Dame, USA
Xinfu Chen; Bei Hu. Viscosity solutions of discontinuous Hamilton–Jacobi equations. Interfaces and free boundaries, Tome 10 (2008) no. 3, pp. 339-359. doi: 10.4171/ifb/192
@article{10_4171_ifb_192,
author = {Xinfu Chen and Bei Hu},
title = {Viscosity solutions of discontinuous {Hamilton{\textendash}Jacobi} equations},
journal = {Interfaces and free boundaries},
pages = {339--359},
year = {2008},
volume = {10},
number = {3},
doi = {10.4171/ifb/192},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/192/}
}
TY - JOUR
AU - Xinfu Chen
AU - Bei Hu
TI - Viscosity solutions of discontinuous Hamilton–Jacobi equations
JO - Interfaces and free boundaries
PY - 2008
SP - 339
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VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/192/
DO - 10.4171/ifb/192
ID - 10_4171_ifb_192
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