Long time behavior of semilinear wave equation with localized interior damping term under acoustic boundary condition

ŞEN Z., YAYLA S.

Japan Journal of Industrial and Applied Mathematics, vol.40, no.2, pp.1221-1257, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s13160-023-00571-0
  • Journal Name: Japan Journal of Industrial and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.1221-1257
  • Keywords: Wave equation, Global attractor, Acoustic boundary condition
  • Hacettepe University Affiliated: Yes

Abstract

This paper is concerned with the long time dynamics of the semilinear wave equation including localized interior damping term under acoustic boundary conditions. With appropriate assumptions, the existence of a global attractor for the semigroup generated by the considered problem is proved. Moreover, imposing more strict conditions on the nonlinearity in the equation, the regularity and finite dimensionality of the attractor are established.