Abstract.
We deal with the non characteristic initial and boundary value problem for an n × n strictly hyperbolic system of conservation laws in one space dimension
Here F is a smooth vector field defined in an open, convex neighborhood of the origin of \({\mathbb{R}}^n, \bar{u}\) and g are functions with small total variation, \(x = \psi(t)\) is a non characteristic Lipschitz boundary profile, and b a \({\mathcal{C}}^1\) function. We prove that the front tracking solutions to (*) constructed by D. Amadori in [1] are stable for the \({\mathbb{L}}^1\) topology. This implies the existence of a Standard Riemann Semigroup and hence the well-posedness of (*).
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
This work has been partially supported by MIUR-COFIN 2002 Equazioni Iperboliche e Paraboliche Nonlineari
Rights and permissions
About this article
Cite this article
Donadello, C., Marson, A. Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws. Nonlinear differ. equ. appl. 14, 569–592 (2007). https://doi.org/10.1007/s00030-007-5010-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00030-007-5010-7