Solution of the Cauchy problem for a conservation law with a discontinuous flux function

@article{Gimse1992SolutionOT,
  title={Solution of the Cauchy problem for a conservation law with a discontinuous flux function},
  author={Tore Gimse and Nils Henrik Risebro},
  journal={Siam Journal on Mathematical Analysis},
  year={1992},
  volume={23},
  pages={635-648}
}
The Cauchy problem is solved for a conservation law arising in oil reservoir simulation where the flux function may depend discontinuously on the space variable. To do this front tracking is used as a method of analysis. 

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References

SHOWING 1-10 OF 13 REFERENCES

A NUMERICAL METHOD FOR A SYSTEM OF EQUATIONS MODELLING ONE-DIMENSIONAL THREE-PHASE FLOW IN A POROUS MEDIUM

A numerical method for Riemann problems for a class of equations (system of conservation laws) is presented. Stability and convergence in a case of three-phase flow in porous media is shown and the

Fundamentals of numerical reservoir simulation

Riemann problems with a discontinuous fiux function

  • Proceedings from the Third International Conference on Hyperbolic Problems
  • 1990

Risebro, Riemann problems with a discontinuous fiux function, in "Proceedings from the Third International

  • Conference on Hyperbolic Problems," Uppsala,
  • 1990

Analysis of a singular system of conservation laws

  • J. Diff. Eqns
  • 1986