Feeble fish in time-dependent waters and homogenization of the G-equation
Optimization and Control
2019-04-18 v3 Analysis of PDEs
Metric Geometry
Abstract
We study the following control problem. A fish with bounded aquatic locomotion speed swims in fast waters. Can this fish, under reasonable assumptions, get to a desired destination? It can, even if the flow is time-dependent. Moreover, given a prescribed sufficiently large time , it can be there at exactly the time . The major difference from our previous work is the time-dependence of the flow. We also give an application to homogenization of the G-equation.
Cite
@article{arxiv.1712.08395,
title = {Feeble fish in time-dependent waters and homogenization of the G-equation},
author = {Dmitri Burago and Sergei Ivanov and Alexei Novikov},
journal= {arXiv preprint arXiv:1712.08395},
year = {2019}
}
Comments
final version, to appear in Comm. Pure Appl. Math