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Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data
Let u be a solution to a quasi-linear Klein-Gordon equation in one-space dimension, $\Box u + u = P (u, $\partial$\_t u, $\partial$\_x u; $\partial$\_t $\partial$\_x u, $\partial$^2\_x u)$ , where P is a homogeneous polynomial of degree three, and with smooth Cauchy data of size $ε\rightarrow 0$. It is …