Convergence of a blow-up curve for a semilinear wave equation

We consider a blow-up phenomenon for ∂_t²uε −ε²∂_x²uε = F(∂tuε). The derivative of the solution ∂tuε blows-up on a curve t = Tε(x) if we impose some conditions on the initial values and the nonlinear term F. We call Tε blow-up curve for ∂_t²uε −ε²∂_x²uε = F(∂tuε). In the same way, we consider the blow-up curve t = T-(x) for ∂_t²u = F(∂tu). The purpose of this paper is to show that, for each x, Tε(x) converges to T-(x) as ε → 0.