含弱阻尼和源项的非线性波方程的初边值问题

Global nonexistence for the wave equation with damping and source terms

研究了含弱阻尼和源项的非线性波方程初边值问题.利用势阱理论和凹方法,证明当初始能量E(0)满足0<E(0)<d时(其中d为势阱深度)整体解的不存在性.

The initial boundary value problem of the nonlinear wave equation with the weak damping term and a source term was studied. Using the potential well theory and concavity method, noncontinuation （or blow up） of solutions with the initial energy E（0） satisfying 0〈E（0）〈d（where d being the depth of the potential well） was proved.