Unconditional small data global well-posedness for nonlinear beam equations with weak damping. (June 2018)

• Record Type: Journal Article
• Authors: Takeda, Hiroshi
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 1
• Page End: 33
• Publication Date: 2018-06
• Subjects: Unconditional global well-posed -- Cauchy problem -- Fourth order wave equation with damping -- Large time behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.10.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate the large time behavior of a global solution for the nonlinear beam equation with a weak damping term in weighted Sobolev spaces. We proved the unconditional global well-posedness for small initial data and sharp decay estimates of the global solution in the same framework. The crucial part of our proof is a smoothing effect from the linear principal part to overcome the regularity loss structure in the weighted estimates.