Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian

Abstract

In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian. First, the existence and uniqueness of the local solution are established by the Banach fixed point theorem. Then, the global existence and finite time blowup of the solution are derived at the subcritical and critical initial energy levels. Finally, the finite time blowup of the solution and upper bound and lower bound estimate of blowup time are given at the arbitrarily positive initial energy level.

Keywords

• kirchhoff-type wave equation
• fractional laplacian
• global existence
• finite time blowup
• asymptotic behavior
• blowup time
• 35r11
• 35l05
• 35a01
• 35b40
• 35b44