Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417285 | Journal of Differential Equations | 2011 | 15 Pages |
Abstract
We consider the one-dimensional ordinary differential equation with a vector field which is merely continuous and nonnegative, and satisfies a condition on the amount of zeros. Although it is classically known that this problem lacks uniqueness of classical trajectories, we show that there is uniqueness for the so-called regular Lagrangian flow (by now usual notion of flow in nonsmooth situations), as well as uniqueness of distributional solutions for the associated continuity equation. The proof relies on a space reparametrization argument around the zeros of the vector field.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gianluca Crippa,