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.
Galstyan, Anahit and Yagdjian, Karen, "The global existence of small self-interacting scalar field propagating in the contracting universe" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 30.
Nonlinear Differential Equations and Applications NoDEA