## Abstract

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.

Original language | English |
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Pages (from-to) | 5933-5960 |

Number of pages | 28 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 75 |

Issue number | 15 |

DOIs | |

State | Published - Oct 2012 |

## Keywords

- Entropy solution
- Generalized Glimm scheme
- Hyperbolic integro-differential systems
- Initial-boundary value problem
- Modified Lax method
- Nonlinear balance laws
- Perturbed Riemann problem
- Perturbed boundary Riemann problem
- p-systems