Blow up result for a viscoelatic plate equation with nonlinear source

Abstract

We consider a viscoelastic plate equation with nonlinear source and partially hinged boundary conditions. Our goal is to show analytically that the solution blows up in finite time. The background of the problem comes from the modeling of the downward displacement of suspension bridge using a thin rectangular plate. This result shows that in the present of a nonlinear source such as the earthquake shocks, the bridge will collapse in finite time