On a decay rate for nonlinear extensible viscoelastic beams with history setting. Issue 11 (18th August 2018)

• Record Type: Journal Article
• Authors: Gomes Tavares, E. H.; Jorge Silva, M. A.; Narciso, V.
• Is Part Of: Applicable analysis. Volume 97:Issue 11(2018)
• Page Start: 1916
• Page End: 1932
• Publication Date: 2018-08-18
• Subjects: Extensible beams -- viscoelastic models -- well-posedness -- decay rates; 35B35 -- 35B40 -- 35L76 -- 74D99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1343940
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: In this paper we deal with a nonlinear extensible viscoelastic beam model whose memory term is considered in a history setting. The goal is to extend an approach on stability first provided by Guesmia and Messaoudi (J Math Anal Appl. 2014;416:212–228) to a class of viscoelastic beams/plates with nonlinear extensible and source terms. Our stability result contributes in clarifying how the constants appearing in the decay rate depend upon the nonlinearities and the size of initial data. Thus, it also complements some results dealing with this methodology.