一类非线性四阶波动方程整体弱解的存在性

摘要

讨论一类非线性四阶波动方程的初边值问题.依据位势井理论和紧致性方法,通过构造稳定集,证明当初值属于稳定集,初始能量为正但有适当上界时整体弱解的存在性.%The initial boundary-value problem was discussed for a class of nonlinear fourth-order wave equation. According to potential well theory and compactness method and by means of constructing stable set, the existence of global weak solution was proved when the initial value stayed in the stable set and the positive initial energy was positive with appropriate upper limit.