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Matematicheskie Zametki, 2009, Volume 85, Issue 5, Pages 745–753
DOI: https://doi.org/10.4213/mzm6911 (Mi mzm6911) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Limit Behavior of the Trajectory Attractor of a Nonlinear Hyperbolic Equation Containing a Small Parameter at the Highest Derivative

A. S. Lyapin

Moscow State Aviation Technological University
Full-text PDF (420 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm6911
Abstract: We study the trajectory attractor of a nonlinear nonautonomous hyperbolic equation with dissipation depending on a small parameter. The nonlinear function appearing in this equation does not satisfy the Lipschitz condition. It is shown that, as the small parameter tends to zero, the trajectory attractor of the hyperbolic equation converges to the trajectory attractor of the limit parabolic equation in the corresponding topology.
Keywords: nonlinear hyperbolic equation, trajectory attractor, dissipation, Lipschitz condition, Cauchy problem, translation compactness, attracting set.
Received: 22.08.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 5, Pages 712–719
DOI: https://doi.org/10.1134/S0001434609050113
Bibliographic databases:
UDC: 517.928.4
Language: Russian
Citation: A. S. Lyapin, “On the Limit Behavior of the Trajectory Attractor of a Nonlinear Hyperbolic Equation Containing a Small Parameter at the Highest Derivative”, Mat. Zametki, 85:5 (2009), 745–753; Math. Notes, 85:5 (2009), 712–719
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. Peng Gao, “Asymptotic analysis for semilinear heat equation with hyperbolic perturbation and random fast oscillating noise”, Journal of Differential Equations, 431 (2025), 113215  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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