一类非线性异号源项波动方程弱解的存在性

Existence of Weak Solutions for a Class of Nonlinear Signs of Source Terms

研究了一类非线性异号源项波动方程的初边值问题。由于能量是非正定的,传统的Galerkin方法无法得到先验估计。应用位势井方法得到了不具有正定能量情况下问题整体弱解的存在性。证明了对于非线性项的指数在一定条件下,问题存在整体弱解,补充和推广了现有结论。

In this paper, the initial boundary value problem for a class of nonlinear wave equation with different sign source terms is studied. However, the energy is non-positive, it is hard to obtain the priori estimate by using the traditional Galerkin method. Therefore, the application of the potential well method gives the existence of the overall weak solution of the problem without positive energy. It is proved that there is a global weak solution for the exponential of nonlinear term under certain conditions. The existing conclusions are supplemented and generalized.