具色散非线性波动方程解的存在性与爆破

The existence and blow-up of solutions for nonlinear wave equations with dispersion term

研究了一类非线性波动方程初边值问题整体解的存在性与爆破问题.利用位势井方法证明了具有两个异号源和具有四阶色散项的波动方程在方程具有负定能量情形下初边值问题整体解的存在性.利用凹性方法证明了具有任意初始正能量时解的有限时间爆破问题.

The global existence and blow up of solutions for a class of nonlinear wave equations is studied in this paper.By employing potential well method,the existence of global solutions for initial boundary value problem with two different sign sources and dispersion term in the presence of negative definite energy is proved.The finite time blow up of solutions with arbitrary initial positive energy is also discussed by using the concavity method.