Global exact boundary controllability for cubic semi-linear wave equations and Klein-Gordon equations

2009 ◽  
Vol 31 (1) ◽  
pp. 35-58 ◽  
Author(s):  
Yi Zhou ◽  
Wei Xu ◽  
Zhen Lei
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Exact Boundary ◽  
Klein Gordon ◽  
Linear Wave Equations

scholarly journals On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains

2020 ◽  
Vol 21 (2) ◽  
pp. 371
Author(s):  
R. S. O. Nunes
Keyword(s):  
Initial Data ◽  
Wave Operator ◽  
Gordon Equation ◽  
Controllability Problem ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Exact Boundary ◽  
Cylindrical Domains ◽  
Klein Gordon ◽  
Klein Gordon Equation

The purpose of this paper is to study an exact boundary controllability problem in noncylindrical domains for the linear Klein-Gordon equation. Here, we work near of the extension techniques presented By J. Lagnese in [12] which is based in the Russell’s controllability method. The control time is obtained in any time greater then the value of the diameter of the domain on which the initial data are supported. The control is square integrable and acts on whole boundary and it is given by conormal derivative associated with the above-referenced wave operator.

A CLASS OF SPECIAL EXACT SOLUTIONS OF SOME HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4563-4579 ◽  
Author(s):  
DENG-SHAN WANG
Keyword(s):  
Exact Solutions ◽  
Wave Equations ◽  
Toda Lattice ◽  
Gordon Equation ◽  
High Dimensional ◽  
Linear Wave ◽  
Non Linear ◽  
Klein Gordon ◽  
Linear Wave Equations ◽  
Toda Lattice Equation

In this paper, the separation transformation approach is extended to some high dimensional non-linear wave equations, such as the (N+1)-dimensional Zhiber–Shabat equation, the generalized (N+1)-dimensional complex non-linear Klein–Gordon equation and the generalized (N+1)-dimensional Toda lattice equation. As a result, a class of special exact solutions of these equations are obtained. The solutions obtained contain one or two arbitrary functions which may lead to abundant structures of the high dimensional non-linear wave equations.

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