Feeble Fish in Time‐Dependent Waters and Homogenization of the G‐equation | Zendy

Burago Dmitri | Zendy; Ivanov Sergei | Zendy; Novikov Alexei | Zendy

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

Author(s) -

Burago Dmitri,

Ivanov Sergei,

Novikov Alexei

Publication year - 2020

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21878

Subject(s) - homogenization (climate) , bounded function , mathematics , fish <actinopterygii> , dynamic equation , fishery , mathematical analysis , ecology , physics , biology , biodiversity , nonlinear system , quantum mechanics

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. © 2019 Wiley Periodicals, Inc.

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