ov 2 00 5 Vanishing viscosity solutions of a 2 × 2 triangular hyperbolic system with Dirichlet conditions on two boundaries

@inproceedings{Spinolo2005ov20,
  title={ov 2 00 5 Vanishing viscosity solutions of a 2 × 2 triangular hyperbolic system with Dirichlet conditions on two boundaries},
  author={Laura V. Spinolo},
  year={2005}
}
on a domain (t, x) ∈ ]0, +∞[×]0, l[ with Dirichlet boundary conditions imposed at x = 0 and at x = l. The matrix A is assumed to be in triangular form and strictly hyperbolic, and the boundary is not characteristic, i.e. the eigenvalues of A are different from 0. We show that, if the initial and boundary data have sufficiently small total variation, then the solution u exists for all t ≥ 0 and depends Lipschitz continuously in L on the initial and boundary data. Moreover, as ε → 0, the… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.
3 Citations
21 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 21 references

Vanishing viscosity solutions for general hyperbolic systems with boundary

  • F. Ancona, S. Bianchini
  • Preprint IAC-CNR 28
  • 2003
Highly Influential
9 Excerpts

The unique limit of the Glimm scheme

  • A. Bressan
  • Arch. Rational Mech. Anal., 130:205–230
  • 1995
Highly Influential
4 Excerpts

The Riemann Problem for General Systems of Conservation Laws

  • T. P. Liu
  • J. Differential Equations, 18:218–234
  • 1975
Highly Influential
3 Excerpts

Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws

  • C. Donadello, A. Marson
  • Preprint
  • 2005
2 Excerpts

A case study in vanishing viscosity

  • S. Bianchini, A. Bressan
  • Discrete Contin. Dynam. Systems, 7:449–476
  • 2001
1 Excerpt

BV estimates for a class of viscous hyperbolic systems

  • S. Bianchini, A. Bressan
  • Indiana Univ. Math. J., 49:1673–1713
  • 2000
2 Excerpts

Well-posedness of the Cauchy problem for n×n conservation laws

  • A. Bressan, G. Crasta, B. Piccoli
  • Mem. Amer. Math. Soc., 694
  • 2000
1 Excerpt

Olenik type estimates and uniqueness for n× n conservation laws

  • A. Bressan, P. Goatin
  • J. Differential Equations, 156:26–49
  • 1999
1 Excerpt

Similar Papers

Loading similar papers…