scholarly journals Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions

2015 ◽  
Vol 368 (1) ◽  
pp. 27-87 ◽  
Author(s):  
Frank Merle ◽  
Hatem Zaag
Keyword(s):  
Wave Equation ◽  
Higher Dimensions ◽  
Stationary Solutions ◽  
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.

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

scholarly journals Semilinear wave equation on manifolds

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