Blow-up Of Solutions For Nonlinear Wave Equation With Boundary Damping

The partial differential equations can be traced to the 18th century, and it is still one of the most popular topics. In the last century, many mathematic scientists have proven some properties of different partial differential equations’ solutions, such as existence, uniqueness, stability and so on. Especially, many mathematic scientists and researchers made a compre-hensive research about the properties of wave equation’s solution, such as the uniqueness, global existence, local existence, stabilities, exponential decay, polynomial decay and other important conclusion.This thesis mainly studies the solution’s blow-up of nonlinear wave equation with bound-ary damping, source terms and the different primary energy. The first problem which this thesis investigate is about the blow-up of the solutions for nonlinear wave equation with boundary damping and internal source, thus the sufficient condition of blow-up the solutions for that equation with positive initial energy and the estimate of the finite blow-up time are obtained. The second problem is about the blow-up of the solutions for the nonlinear wave equation with interior damping, we also conclude both the sufficient condition of blow-up of the solution with negative initial energy and the estimate of the finite blow-up time.