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.
|Number of pages||11|
|Journal||Discrete and Continuous Dynamical Systems - Series S|
|Publication status||Published - 2021 Mar|
- Numerical analysis
- Wave equation