Stabilization of a Semilinear Wave Equation with Delay

Author(s):  
Victor Hugo Gonzalez Martinez ◽  
Talita Druziani Marchiori ◽  
Alisson Younio de Souza Franco
2020 ◽  
Vol 26 ◽  
pp. 7
Author(s):  
Hui Wei ◽  
Shuguan Ji

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.


2001 ◽  
Vol 26 (11-12) ◽  
pp. 2267-2303 ◽  
Author(s):  
Charlotte Heiming ◽  
Hideo Kubo ◽  
Vladimir Georgiev

1988 ◽  
Vol 132 (2) ◽  
pp. 215-225 ◽  
Author(s):  
Alfonso Castro ◽  
Sumalee Unsurangsie

2002 ◽  
Vol 11 (1) ◽  
pp. 7-18 ◽  
Author(s):  
F. D. Araruna ◽  
G. O. Antunes ◽  
L. A. Medeiros

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