Decay estimates for the Cauchy problem for the damped extensible beam equation. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Racke, Reinhard; Yoshikawa, Shuji
• Is Part Of: Applicable analysis. Volume 95:Issue 5(2016)
• Page Start: 1118
• Page End: 1136
• Publication Date: 2016-05-03
• Subjects: decay estimate -- extensible beam -- Cauchy problem -- Ball's model -- Kelvin–Voigt damping; 35G10 -- 35B65 -- 35G25 -- 35E05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1053051
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The extensible beam equation proposed by Woinowsky-Krieger is a fourth order dispersive equation with nonlocal nonlinear terms. In this paper we study the Cauchy problem of the extended model by Ball who proposed the following model with external and structural damping terms: For this represents a Kelvin–Voigt damping. We show the unique global existence of solutions for this problem and give a precise description of the decay of solutions in time.