Geodesic
Averaging the Trajectory Attractor of a Nonlinear Wave Equation with Rapidly Oscillating Right-Hand Side
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 390-394

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We consider a nonlinear nonautonomous hyperbolic equation with dissipation and with a small parameter multiplying the highest derivative with respect to time. This equation also involves a rapidly oscillating external force. Using a standard technique for constructing the trajectory attractor, we can prove the convergence of the attractor of a nonlinear nonautonomous hyperbolic equation with dissipation to the attractor of the corresponding parabolic equation.
Keywords: nonlinear wave equation, trajectory attractor, rapidly oscillating external force, Galerkin method.
Mots-clés : parabolic equation 
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     author = {A. S. Lyapin},
     title = {Averaging the {Trajectory} {Attractor} of a {Nonlinear} {Wave} {Equation} with {Rapidly} {Oscillating} {Right-Hand} {Side}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a6/}
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A. S. Lyapin. Averaging the Trajectory Attractor of a Nonlinear Wave Equation with Rapidly Oscillating Right-Hand Side. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 390-394. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a6/