A Class Of Nonlinear Wave Equation Blasting And A Class Of Semi-linear Parabolic Equation Critical Exponent Problems

This thesis consists of three chapters, the first chapter is introduction, the second chapter consider the initial-boundary value problem for the nonlinear wave equation:in a bounded domainIn chapter 2,We investigates the problem withrespectively. By the energy function and potential well method, we proof that the solution blow up in finite time under certain conditions.then there exist a constant number,the solution must blow up.Where:Finally, in chaptr3 ,we study the global existence and blow-up of sign-changing solutions in a semilinear parabolic equationFirstly, we make a self-similar transformation, then consider its eigenvalue problem, we also apply the theory of infinite dimensional dynamical systems. It isshown that for any nonnegative integerk:,pk =1+ (2 + 2q- )/(k + 1)is the critical exponent for the above problem, i.e.then any nontrivial solution withblows up infinite time;,then the problem has a global solution with...