Dynamics of a Cauchy problem related to extensible beams under nonlocal and localized damping effects


YAYLA S. , Cardozo C. L. , Jorge Silva M. A. , Narciso V.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.494, no.1, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 494 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1016/j.jmaa.2020.124620
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Abstract

This paper is devoted to the study of long-time dynamics of a Cauchy problem related to extensible beam models with dissipative effects coming from the nonlocal Balakrishnan-Taylor and the localized weak damping terms in R-n. Our first main result features a new unique continuation property for models associated with extensible beams. Then, applying such a property and with the fundamental aid of the nonlocal Balakrishnan-Taylor damping term, we state and prove our second main result dealing with the existence, characterization and regularity of a compact global attractor for the corresponding nonlinear dynamical system. (C) 2020 Elsevier Inc. All rights reserved.