Blow-up And The Decay Rate Of The Solutions To Three Nonlinear Evolution Equations

The study for the blow-up and decay rate of the solution to nonlinear evolution equation is the one of the important branches of partial differential equation. In this thesis, we will study the blow-up and decay rate of the solutions to three nonlinear evolutions. First, we will use the upper and lower solution method to study the equation , and get the sufficient conditions for the finite time blow up and global existence. And next, we use the Lyapunov type technique to the equation ut , show that the solution energy decay at a similar rate of the decay of the relaxation function. In the end, we use convex method to consider the equation and show that the solution will blow up under arbitrary initial high energy, maybe this is the first time to prove such result for this type equation.