## 摘要

This research explores the initial-boundary value problem for the 2 × 2 hyperbolic systems of balance laws whose sources are the time-dependent and contain the integral of unknowns. Perturbed Riemann and boundary Riemann problems are provided to account for the time-dependence of sources. Their approximation solutions are constructed by modified Lax's method. In addition, we introduce a new version of Glimm scheme (GGS) and study its stability which is proved by the wave interaction estimates in a dissipativity assumption. With the consistency of GGS, the existence of a global weak solution satisfying the entropy inequality is then achieved. Finally the Lipschitz continuous solution to the problem is established by the weak convergence of the residual.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 5933-5960 |

頁數 | 28 |

期刊 | Nonlinear Analysis, Theory, Methods and Applications |

卷 | 75 |

發行號 | 15 |

DOIs | |

出版狀態 | 已出版 - 10月 2012 |