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