Critical and sup-critical initial energy finite time blowup phenomena for the fourth-order wave equations with nonlinear strain term. (September 2020)

• Record Type: Journal Article
• Authors: Lin, Qiang; Shen, Jihong; Wang, Xingchang
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35L05 -- 35A01 -- 35L55; Fourth-order wave equation -- Nonlinear strain -- Blowup -- Potential well; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111873
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is devoted to the blowup phenomena for a class of fourth-order wave equation with nonlinear strain term. First, for the model equation with strain structure, we prove the finite time blowup of solution for the critical initial energy, i.e., E ( 0 ) = d . Then, the finite time blowup and the upper bound of the blowup time are established for the sup-critical initial energy, i.e., E ( 0 ) > 0 .