Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients

By Ferruccio Colombini, D. Santo, T. Kinoshita. 2002

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Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients (2013, background): “) coefficients with a parameter ε, relating ε to some frequency zones in the energy estimate often yields the Gevrey or even C∞ well-posedness (see for example [6,7], and other papers).”
On the asymptotic behavior of the energy for the wave equations with time depending coefficients (2007, background): “[4] considered the well-posedness in the Gevrey class of (1) up to t = T under the assumption |a′(t)| ≤ (T − t)−s (10) for s > 1.”