Abstract
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.
Keywords: Klein-Gordon equation; Cross-constrained variational problem; Global existence; Blowup; Invariant manifold
Published Online: 2016-03-10
Published in Print: 2010-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
