Global Existence and Blowup for the Cubic Nonlinear Klein-Gordon Equations in Three Space Dimensions

作者：Zhang Jian^*; Gan Zaihui; Guo Boling

来源：Advanced Nonlinear Studies, 2010, 10(2): 315-329.

• Klein-Gordon equation
• Cross-constrained variational problem
• Global existence
• Blowup
• Invariant manifold

In this paper, we apply a cross-constrained variational method to study the classic nonlinear Klein-Gordon equation with cubic nonlinearity in three space dimensions. By constructing a type of cross-constrained variational problem and establishing the so-called cross invariant manifolds, we obtain a sharp threshold for blowup and global existence of the solution to the equation under study which is different from that in [10]. On the other hand, we give an answer to the question that how small the initial data have to be for the global solutions to exist.

• 出版日期2010-5
• 单位四川师范大学; 北京应用物理与计算数学研究所