An Engquist-Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections

@article{Brger2009AnES,
  title={An Engquist-Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections},
  author={Raimund B{\"u}rger and Kenneth H. Karlsen and John D. Towers},
  journal={SIAM J. Numerical Analysis},
  year={2009},
  volume={47},
  pages={1684-1712}
}
We consider scalar conservation laws with the spatially varying flux H(x)f(u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L1 contraction semigroups, one for each so-called connection (A, B). Here we define entropy solutions of type (A, B) involving Kružkov-type entropy inequalities that can be adapted to any… CONTINUE READING
27 Citations
43 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 27 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 43 references

Optimal entropy solutions for conservation laws with discontinuous flux functions

  • Adimurthi, S. Mishra, G. D. Veerappa Gowda
  • J. Hyperbolic Differ. Equ.,
  • 2005
Highly Influential
13 Excerpts

Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies

  • E. Audusse, B. Perthame
  • Proc. Roy. Soc. Edinburgh Sect. A,
  • 2005
Highly Influential
13 Excerpts

Existence of strong traces for generalized solutions of multidimensional scalar conservation laws

  • E. Y. Panov
  • J. Hyperbolic Differ. Equ.,
  • 2005
Highly Influential
5 Excerpts

Towers. L1 stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients

  • K. H. Karlsen, N. H. Risebro, J.D
  • Skr. K. Nor. Vid. Selsk
  • 2003
Highly Influential
10 Excerpts

Hydrodynamic limit for particle systems and related conservation laws with discontinuous fluxes

  • G.-Q. Chen, N. Even, C. Klingenberg
  • In preparation,
  • 2007
Highly Influential
5 Excerpts

Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux

  • K. H. Karlsen, J. D. Towers
  • Chin. Ann. Math.,
  • 2004
Highly Influential
6 Excerpts

Similar Papers

Loading similar papers…