Feeble Fish in Time‐Dependent Waters and Homogenization of the G‐equation
Dmitri Burago, Sergei Ivanov, Alexei Novikov · Communications on Pure and Applied Mathematics · 2019
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 timet, it can be there at exactly the timet. 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. © 2019 Wiley Periodicals, Inc.