Numerical study on formation of an acoustic soliton in bubbly liquids based on weakly nonlinear wave equation

2019 ◽  
Vol 146 (4) ◽  
pp. 3077-3077
Author(s):  
Takahiro Ayukai ◽  
Tetsuya Kanagawa
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Numerical Study ◽  
Weakly Nonlinear ◽  
Bubbly Liquids

scholarly journals The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

2020 ◽  
Vol 13 (2) ◽  
pp. 314-322
Author(s):  
Gunay Ismayilova
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Necessary Condition ◽  
Weakly Nonlinear ◽  
Necessary Condition Of Optimality

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

scholarly journals Nonlinear Wave Equation for Ultrasound Beam in Nonuniform Bubbly Liquids

2011 ◽  
Vol 6 (2) ◽  
pp. 279-290 ◽  
Author(s):  
Tetsuya KANAGAWA ◽  
Takeru YANO ◽  
Masao WATANABE ◽  
Shigeo FUJIKAWA
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Ultrasound Beam ◽  
Bubbly Liquids
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