An Approximate Periodic Solution of a Weakly Nonlinear Wave Equation

1976 ◽  
Vol 43 (3) ◽  
pp. 504-505
Author(s):  
D. A. Sa´nchez
Keyword(s):  
Periodic Solution ◽  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Weakly Nonlinear

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.

Periodic solutions of a nonlinear wave equation

1980 ◽  
Vol 85 (3-4) ◽  
pp. 313-320 ◽  
Author(s):  
Abbas Bahri ◽  
Haïm Brezis
Keyword(s):  
Periodic Solution ◽  
Wave Equation ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Linear Growth ◽  
Necessary Condition ◽  
Image Position

SynopsisWe provide a sufficient and “almost” necessary condition for the existence of a periodic solution of the equationwhere F is nondecreasing in u and has a small linear growth as |u|→∞.

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