Formation and construction of large variational shock waves for 1-D n n quasilinear hyperbolic conservation systems

In the paper Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinearity 38 (2025), No. 2, 025016, for the 1-D n n (n 3) strictly hyperbolic system ₜv+F (v) ₓv=0 with some classes of large variational initial data v (x, 0), the geometric blowup mechanism and the detailed singularity behaviours of ₗ, ₓv near the blowup point are studied when the n n matrix F (v) admits at least one genuinely nonlinear eigenvalue. In this paper, we focus on the formation and construction of a large variational shock wave from the blowup point for 1-D n n quasilinear hyperbolic conservation law system ₜu+ₓf (u) =0 when some smooth simple wave solution is generic non-degenerate before the formation of singularity and the corresponding eigenvalue is genuinely nonlinear.