scholarly journals A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects

Wave Motion ◽  
2022 ◽  
pp. 102876
Author(s):  
M. Scholle
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Acoustic Waves ◽  
Weakly Nonlinear ◽  
Non Equilibrium

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.

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