三维有界区域上临界半线性波动方程解的爆破问题

摘要

研究三维空间中有界区域上具有聚焦型非线性项的临界半线性波动方程解的破裂，它适用于狄利克雷和耗散边界条件情形。在证明主要结论的过程中用到了凹方法，它是在20世纪70年代由Levine-Payne引入的。此外，还构造了一种新的具有指数型参数β的辅助函数，以确保结果对任意初始能量都成立。%In this paper,we establish blow up theorems for critical semilinear wave equations with focusing nonlinear term in 3-D bounded domains,for both Dirichlet and dissipative boundary conditions. Concavity method is used to prove the main results,which was introduced by Levine-Payne in 1970s. Also,a new auxiliary function with parameter β of exponential type is constructed,in order to guarantee that the results hold without any assumption on the initial data and initial energy.