TY - JOUR
T1 - On the Occurrence of "Vacuum States" for 2 $\times$ 2 Quasilinear Hyperbolic Conservation Laws
AU - Lin , Longwei
JO - Journal of Partial Differential Equations
VL - 1
SP - 64
EP - 72
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5639.html
KW - “Vacuum states” quasilinear hyperbolic conservation laws
AB -  We show that the solution Lo the Cauchy problem of 2 × 2 nonlinear conservation laws, in general, may go out the strictly hyperbolic region of the system in a finite time, here the initial data are given in the strictly hyperbolic region. In other words, in general, we can't confine our attention to solve the Cauthy problem of 2 × 2 nonlinear consenvation laws in strictly hyperbolic type. However, we can expect that it may be solved under the additional conditions (A) and (b).