Uniqueness Results for Nonlocal Hamilton-Jacobi Equations

Details Uniqueness Results for Nonlocal Hamilton-Jacobi Equations Uniqueness Results for Nonlocal Hamilton-Jacobi Equations

2008-03-17

arxiv.org/abs/0803.2480v1

Journal of Functional Analysis 257, 5 (2009) 1261-1287

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.jfa.2009.04.014

We are interested in nonlocal Eikonal Equations describing the evolution of interfaces moving with a nonlocal, non monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.

Affiliated with

Also associated with

No associations

Rating

Uniqueness Results for Nonlocal Hamilton-Jacobi Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniqueness Results for Nonlocal Hamilton-Jacobi Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniqueness Results for Nonlocal Hamilton-Jacobi Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-646456