Taro Yamanoi

Asymptotic Formula of the Lifespan of Classical Solutions to 1D Quasilinear Wave Equations

We study the lifespan \(T^*(\varepsilon)\) of classical solutions to the Cauchy problem for the one-dimensional quasilinear wave equation $u_{tt}-(c(u)^2u_x)_x=0$, with initial data of size $\varepsilon>0$. We assume that $c'(\theta)\sim a|\theta|^{p-2}$ as $\theta \to 0$, where \(a>0\) and \(p>3\) or $p=2$. We obtain...