Finite Time Blow-up Of Solutions To Some Evolution Equations

In this dissertation,we focus on the finite time blow-up of the solutions to some evolution equations,including semilinear wave equations,Navier-Stokes-Poisson equations in fluid mechanics and semilinear heat equations.In the first part,by using the cut-off function and a special solution of the linear wave equation,we construct a test function,which is negative itself but has nonnegative derivative with respect to the time variable.In the second part,finite time blow-up result of the energy solution of the unipolar Navier-Stokes-Poisson equation is established.Firstly,the energy inequality is established,and then the mass and momentum conservation identities are established according to the equation,and finally,we obtain blow-up result by contradiction argument.In the third part,for the initial boundary value problem of the semi-linear wave equation with Neumann boundary conditions in exterior domain,by constructing an appropriate test function,the upper bound of lifespan of the solution is obtained.In the fourth part,for the semi-linear heat equation,using the heat kernal as a test function,the finite time blow-up result and the upper bound of lifespan are established.