Global well-posedness of fourth-order Petrovsky equation with weak and strong damping terms

Abstract

In this paper, a semilinear fourth-order Petrovsky equation with nonlinear weak damping term and linear strong damping term is considered in the frame of the potential well. We prove the existence and uniqueness of the global strong solution with sub-critical initial energy. In addition, we obtain the global existence, asymptotic behaviour and finite time blowup for the weak (non-steady state) solution with a critical initial energy level.

Keywords:

• Petrovsky equation
• global strong solution
• weak solution
• asymptotic behavior
• finite time blowup

AMS Classifications:

• 35L35
• 35B40
• 35D30
• 35D35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities (3072021CF2404), the Fundamental Research Funds for the Central Universities.