Asymptotic behavior and finite time blow up for damped fourth order nonlinear evolution equation

Article type: Research Article

Authors: Han, Jiangbo | Xu, Runzhang | Yang, Yanbing^{; *}

Affiliations: College of Mathematical Sciences, Harbin Engineering University, 150001, People’s Republic of China. E-mails: [email protected], [email protected], [email protected], [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mails: [email protected], [email protected].

Abstract: This paper investigates the initial boundary value problem for a class of fourth order nonlinear damped wave equations modeling longitudinal motion of an elasto-plastic bar. By applying a suitable potential well-convexity method, we derive the global existence, asymptotic behavior and finite time blow up for the considered problem with more generalized nonlinear functions at subcritical initial energy level. Further for arbitrarily positive initial energy we give some sufficient conditions ensuring finite time blow up.

Keywords: Fourth order damped wave equation, asymptotic behavior, finite time blow up, arbitrarily positive initial energy

DOI: 10.3233/ASY-201621

Journal: Asymptotic Analysis, vol. 122, no. 3-4, pp. 349-369, 2021