On One Control Problem for Zakharov–Kuznetsov Equation

An initial-boundary value problem for Zakharov–Kuznetsov equation u t + bu x + u xxx + u xyy + uu x = f 0 (t)g(t, x, y) posed on a rectangle (0, R) × (0, L) for t ∈ (0, T) under certain initial and boundary conditions is considered. Here, the function f 0 is unknown and is referred as a control, and the function g is given. The problem is to find a pair (f 0 , u), satisfying the additional condition ∫0Tu(t,x,y)ω(x,y)dxdy=φ(t), where the functions ω, φ are given and u is the solution to the corresponding initial-boundary value problem. It is shown that under certain smallness assumptions on input data such a pair exists and is unique. For the corresponding linearized equation, a similar result is obtained without any smallness assumptions. © Springer Nature Switzerland AG 2019.

Authors
Editors
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Collection of articles
Publisher
Springer International Publishing
Number of issue
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Language
English
Pages
305-313
Status
Published
Department
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Link
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Number
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Volume
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Year
2019
Organizations
  • 1 RUDN University, Moscow, Russian Federation
Keywords
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Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38950/