This article is cited in 2 papers

Averaging the Trajectory Attractor of a Nonlinear Wave Equation with Rapidly Oscillating Right-Hand Side

A. S. Lyapin

Moscow State Aviation Technological University

Abstract: 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, parabolic equation, rapidly oscillating external force, Galerkin method.

UDC: 517.958

Received: 16.03.2007

DOI: 10.4213/mzm3851

 English version: Mathematical Notes, 2007, 82:3, 347–351

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