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<p>We investigate the forward dynamics of a nonautonomous semilinear wave-type evolution problem, which models propagation phenomena in nonlinear elastic rods and ion-acoustic waves. We establish global well-posedness and prove the existence of a family of uniform attractors under appropriate growth and dissipativity conditions. Additionally, we demonstrate upper-semicontinuity in a suitable space and derive regularity results in a more refined space. Finally, we characterize the uniform attractor through kernel sections for the problem under consideration.</p>

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Existence, regularization and upper-semicontinuity of uniform attractors for a nonautonomous semilinear evolution equation of second order

  • 期刊论文

  • 发表日期：

    2025年8月17日

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  • Vinicius T. Azevedo,
  • Everaldo M. Bonotto,
  • Arthur C. Cunha,
  • Marcelo J. D. Nascimento

摘要

We investigate the forward dynamics of a nonautonomous semilinear wave-type evolution problem, which models propagation phenomena in nonlinear elastic rods and ion-acoustic waves. We establish global well-posedness and prove the existence of a family of uniform attractors under appropriate growth and dissipativity conditions. Additionally, we demonstrate upper-semicontinuity in a suitable space and derive regularity results in a more refined space. Finally, we characterize the uniform attractor through kernel sections for the problem under consideration.