Mechanism of the Formation of Singularities to the Goursat Problem for Diagonal Systems with Linearly Degenerate Characteristic Fields

摘要

For an inhomogeneous quasilinear hyperbolic system of diagonal form,under the assumptions that the system is linearly degenerate and the C1 norm of the boundary data is bounded,we show that the mechanism of the formation of singularities of C1 classical solution to the Goursat problem with C1 compatibility conditions at the origin must be an ODE type.The similar result is also obtained for the weakly discontinuous solution with C0 compatibility conditions at the origin.