Blow Up Of Solutions To The Cauchy Problem For Several Classes Of Semilinear Wave Equations

The thesis concerns with the blow up of solutions to the Cauchy problem for semi-linear wave equations.First of all,we consider the solutions to the Cauchy problem for semilinear wave equations with constant coefficients.By utilizing the method of an iteration argument,we obtain the blow up and the lower bound of lifespan of solutions to the Cauchy problem for semilinear wave equations;At the same time,the semilinear hyperbolic Yamabe problem in low dimension case is studied by using the known results,and the blow up characterization of solutions to the cauchy problem is given.Then,we consider two classes of semilinear wave equations with variable coefficients.By constructing test functions and using the results of Riccati equation,we obtain the blow up and the upper bound of lifespan of solutions to the Cauchy problem for the semilinear wave equations with variable coefficients.