Local uniform stability for the semilinear wave equation in inhomogeneous media with locally distributed Kelvin-Voigt damping

2018 ◽  
Vol 291 (14-15) ◽  
pp. 2145-2159 ◽  
Author(s):  
M. Astudillo ◽  
M. M. Cavalcanti ◽  
R. Fukuoka ◽  
V. H. Gonzalez Martinez
Keyword(s):  
Wave Equation ◽  
Inhomogeneous Media ◽  
Uniform Stability ◽  
Semilinear Wave Equation

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.

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

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

scholarly journals A semilinear wave equation with nonmonotone nonlinearity

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