Volume 8, Issue 1
On the Occurrence of "Vacuum States" for 2 $\times$ 2 Quasilinear Hyperbolic Conservation Laws

Longwei Lin

DOI:

J. Part. Diff. Eq., 8 (1995), pp. 64-72.

Published online: 1995-08

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  • Abstract

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).

  • Keywords

“Vacuum states” quasilinear hyperbolic conservation laws

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@Article{JPDE-8-64, author = {Lin , Longwei }, title = {On the Occurrence of "Vacuum States" for 2 $\times$ 2 Quasilinear Hyperbolic Conservation Laws}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {1}, pages = {64--72}, abstract = { 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).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5639.html} }
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).
Longwei Lin . (2019). On the Occurrence of "Vacuum States" for 2 $\times$ 2 Quasilinear Hyperbolic Conservation Laws. Journal of Partial Differential Equations. 8 (1). 64-72. doi:
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