Mechanism of singularity formation for quasilinear hyperbolic systems with linearly degenerate characteristic fields

摘要

For the Cauchy problem of 1-D first order quasilinear hyperbolic linearly degenerate systems, a new mechanism of singularity formation is given to show that all the W~(1,p) (1≤+~∞) norms of the C1 solution should blow up simultaneously. It gives a way to verify the property of ODE singularity by directly using the energy method in the framework of C1 solution.