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-Lamaˆitre-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.
Galstian, A., Yagdjian, K. The global existence of small self-interacting scalar field propagating in the contracting universe. Nonlinear Differ. Equ. Appl. 27, 28 (2020). https://doi.org/10.1007/s00030-020-00632-0
Nonlinear Differential Equations and Applications NoDEA