A variational method for the numerical simulation of a boundary controllability problem for the linear and semilinear 1D wave equations

2014 ◽  
Vol 351 (7) ◽  
pp. 3865-3882 ◽  
Author(s):  
Ernesto Aranda ◽  
Pablo Pedregal
Keyword(s):  
Numerical Simulation ◽  
Variational Method ◽  
Wave Equations ◽  
Controllability Problem ◽  
Boundary Controllability

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.

scholarly journals Boundary Controllability of a Pseudoparabolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qiang Tao ◽  
Hang Gao ◽  
Zheng-an Yao
Keyword(s):  
Explicit Solution ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Pseudoparabolic Equation ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Boundary Controls ◽  
Controllability Property

We deal with the controllability problem for the pseudoparabolic equation by means of boundary controls. Due to the unusual spectrum of this kind of equations, we prove that the null controllability property is false. Furthermore, by the explicit solution, we show that the approximate controllability holds.

scholarly journals Interaction of Solitons for Sine-Gordon-Type Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Georgii A. Omel’yanov ◽  
Israel Segundo-Caballero
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Wave Equations ◽  
Gordon Equation ◽  
Sine Gordon Equation ◽  
Semilinear Wave Equations ◽  
The Subject ◽  
Interaction Of Solitons

The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions.

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