scholarly journals Exact controllability for a semilinear wave equation with both interior and boundary controls

2005 ◽  
Vol 2005 (6) ◽  
pp. 619-637 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Wave Equation ◽  
Exact Controllability ◽  
Open Domain ◽  
Semilinear Wave Equation ◽  
Boundary Controls ◽  
Feedback Laws

The exact controllability of a semilinear wave equation in a bounded open domain ofRn, with controls on a part of the boundary and in the interior, is shown. Feedback laws are established.

scholarly journals Infinitely many periodic solutions for a semilinear wave equation with x-dependent coefficients

2020 ◽  
Vol 26 ◽  
pp. 7
Author(s):  
Hui Wei ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Spectral Properties ◽  
Seismic Waves ◽  
Forced Vibrations ◽  
One Dimensional ◽  
Semilinear Wave Equation ◽  
Spatial Interval ◽  
Rational Multiple ◽  
Infinitely Many Periodic Solutions

This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with x-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By combining variational methods with an approximation argument, we prove that there exist infinitely many periodic solutions whenever the period is a rational multiple of the length of the spatial interval. The proof is essentially based on the spectral properties of the wave operator with x-dependent coefficients.

SUPERCRITICAL SEMILINEAR WAVE EQUATION WITH NON-NEGATIVE POTENTIAL

2001 ◽  
Vol 26 (11-12) ◽  
pp. 2267-2303 ◽  
Author(s):  
Charlotte Heiming ◽  
Hideo Kubo ◽  
Vladimir Georgiev
Keyword(s):  
Wave Equation ◽  
Negative Potential ◽  
Semilinear Wave Equation
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