The initial-boundary value problem of hyperbolic integro-differential systems of nonlinear balance laws

Shih Wei Chou, John M. Hong, Ying Chin Su

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish
Pages (from-to)5933-5960
Number of pages28
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number15
DOIs
StatePublished - Oct 2012

Keywords

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

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