带加性噪声的随机非线性Klein-Gordon方程

Stochastic Nonlinear Klein-Gordon Equation with Additive Noise

建立了该方程Cauchy问题的局部适定性,在负参数非线性情形下,根据能量方程和Bore-Can-telli引理证明了解都几乎整体存在.在正参数非线性情形下,根据质量方程证明了对于某些情形时,系统的解爆破,所得结论推广了相关文献的结果.

In this paper,firstly,the local well-posedness of the Cauchy problem for the equation is established.Then for the equation with negative parameter nonlinearity,the global existence of solution is proved according to the energy equation and Bore-Cantelli lemma.Finally,for the equation with positive parameter nonlinearity,the solution is proved to blow up with some initial data according to the mass equation.The results obtained in this paper improve some others.