Global existence and blow-up results for a nonlinear model for a dynamic suspension bridge

Abstract

<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>