Abstract:We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lamaître-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.
The Cauchy problem for the Klein–Gordon equation under the quartic potential is considered in the de Sitter spacetime. The existence of global solutions for small rough initial data is shown based on the mechanism of the spontaneous symmetry breaking for the small positive Hubble constant. The effects of the spatial expansion and contraction on the problem are considered.
The Cauchy problem for the Klein–Gordon equation under the quartic potential is considered in the de Sitter spacetime. The existence of global solutions for small rough initial data is shown based on the mechanism of the spontaneous symmetry breaking for the small positive Hubble constant. The effects of the spatial expansion and contraction on the problem are considered.
In the present paper, we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine a result for ordinary differential inequalities with an iteration argument by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.