About the Existence Time of Solutions for Field Equations in the One Space Dimension

Abstract

In this paper, we study the lower bounds problem for the existence time or solutions to the different massive Dinac-Kiein-Gordon equations and with different massive Klein-Gordon equations, in one space dimension, for weakly decaying Cauchy data, of size ε. The results assert that the existence time is (almost) larger than ε^{-4}.