The first part of the paper is devoted to length estimates of the boundary of the reachable set for the plane and state constrained controlled system x'(t) = c(t, x(t)) b(t) (where |b(t)| <= 1 a.e.). This study is motivated in the second part by the analysis of dislocation dynamics, which can be modeled as a curve G( t) moving in an open set O subset of R-2 according to some nonlocal law with Neumann boundary conditions on partial derivative O. The length estimates of the first part play a crucial role in the proof of the existence and uniqueness of a viscosity solution for this model.
Regularity of the eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms
MARCHI, CLAUDIO
2006
Abstract
The first part of the paper is devoted to length estimates of the boundary of the reachable set for the plane and state constrained controlled system x'(t) = c(t, x(t)) b(t) (where |b(t)| <= 1 a.e.). This study is motivated in the second part by the analysis of dislocation dynamics, which can be modeled as a curve G( t) moving in an open set O subset of R-2 according to some nonlocal law with Neumann boundary conditions on partial derivative O. The length estimates of the first part play a crucial role in the proof of the existence and uniqueness of a viscosity solution for this model.File in questo prodotto:
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