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<p>For a certain class of semilinear hyperbolic systems of the first order considered in a multidimensional space-time layer with high frequency terms, among which there are large ones proportional to the square root of the oscillation frequency, the averaging method is justified in the case of the Cauchy problem. In this case, the asymptotic proximity of solutions to the averaged and perturbed problems is uniform in the specified layer.</p>

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AVERAGING OF SEMILINEAR HYPERBOLIC SYSTEMS OF THE FIRST ORDER WITH LARGE HIGH-FREQUENCY TERMS

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • V. B. Levenshtam,
  • A. K. Nazarov

摘要

For a certain class of semilinear hyperbolic systems of the first order considered in a multidimensional space-time layer with high frequency terms, among which there are large ones proportional to the square root of the oscillation frequency, the averaging method is justified in the case of the Cauchy problem. In this case, the asymptotic proximity of solutions to the averaged and perturbed problems is uniform in the specified layer.