The Development of Shock and Cusp for 1D 2×2 Quasilinear Strictly Hyperbolic System With Large Initial Data

ABSTRACT As we all know, for the p‐system with the smooth initial data, the solution will blow up at a finite time and the blowup mechanism corresponds to the geometric blowup. In this paper, we will consider the general 1D quasilinear strictly hyperbolic system, and when the system is genuinely nonlinear with respect to at least one eigenvalue, we can obtain the detailed singularity behavior and the precise preshock. Besides, from the preshock point, not only will a shock form and develop rapidly along the direction of genuine nonlinearity, but there is also a possibility of the occurrence of a cusp singularity in the other direction, regardless of whether the direction is genuinely nonlinear or linearly degenerate.