Blow-up Time Estimation For Solutions Of A Class Of Fourth-order Hyperbolic Equations

In this thesis,we consider the initial and Dirichlet boundary problem of the following fourth-order nonlinear hyperbolic equation with logarithmic and strongly damped terms.We establish a relationship between blow-up property of the solution and the initial energy.Firstly,to give the definition of weak solution.Secondly,it is proved by energy estimation and concave method that the solution blow-up in finite time under low initial energy and high initial energy,and the upper bound of blow-up time is obtained.Finally,a new auxiliary function is constructed,Sobolev embedding theorem and energy inequality are used to obtain the lower bound estimation of blasting time under low initial energy.