Lower And Upper Bounds For The Blow-up Time Of Solutions To A Fourth-order Nonlinear Hyperbolic Equation For Arbitrarily Positive Initial Energy

This paper deals with the initial and Dirichlet boundary problem of the following fourth-order nonlinear hyperbolic equation with sublinear and superlinear sources We give a sufficient condition of initial energy and the initial data when the solution blows up in finite time.Firstly,we apply an energy estimate method and the concavity method to obtain the upper bound to the blow-up time of the equation.Subsequently,we derive the lower bound to the blow-up time by applying interpolation Sobolev inequality and energy inequalities.