Global Solution of the Cauchy Problem for a Class of 2 x 2 Nonstrictly Hyperbolic Conservation Laws *

@inproceedings{Temple1982GlobalSO,
title={Global Solution of the Cauchy Problem for a Class of 2 x 2 Nonstrictly Hyperbolic Conservation Laws *},
author={Blake Temple},
year={1982}
}

We prove the existence of a global weak solution to the Cauchy problem for a class of 2 × 2 equations which model one-dimensional multiphase flow, and which represent a natural generalization of the scalar Buckley-Leverett equation. Loss of strict hyperbolicity (coinciding wave speeds with a (~ I) normal form) occurs on a curve in state space, and waves in a neighborhood of this curve contribute unbounded variation to the approximate Glimm scheme solutions. The unbounded variation is handled by… CONTINUE READING