# American Institute of Mathematical Sciences

March  2003, 2(1): 51-64. doi: 10.3934/cpaa.2003.2.51

## A note on singular limits to hyperbolic systems of conservation laws

 1 IAC-CNR, viale del Policlinico 137, 00161 ROMA, Italy

Received  June 2002 Revised  November 2002 Published  December 2002

In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. Under the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation. The method used here to estimate the source terms is based on the calculus of residues.
Citation: Stefano Bianchini. A note on singular limits to hyperbolic systems of conservation laws. Communications on Pure & Applied Analysis, 2003, 2 (1) : 51-64. doi: 10.3934/cpaa.2003.2.51
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