Existence and nonexistence theorems of global weak solutions to degenerate quasilinear wave equations for the elasticity

We prove the existence and nonexistence of global generalized (nonnegative) solutions of the nonlinearly degenerate wave equations vtt=c(|v|s−1v)xx with the nonnegative initial data v0(x) and s>1. These results are extensions of the results in the second author's paper (Sugiyama, 2016), where the existence and the nonexistence of the unique global classical solution were studied with a threshold on ∫−∞∞v1(x)dx and the non-degeneracy condition v0(x)≥c0>0 on the initial data.