Feeble Fish in Time-Dependent Waters and Homogenization of the G-equation

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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 t, it can be there at exactly the time t. 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.

Original languageEnglish (US)
Pages (from-to)1453-1489
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume73
Issue number7
DOIs
StatePublished - Jul 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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