Preprint 2002-042

Weakly Stable Multi-d Shocks

Abstract: We study the linear stability of multidimensional shock waves for systems of conservation laws in the case where Majda's uniform stability condition is violated. The linearized problem is attacked using the "good unknown" of Alinhac. We prove an energy estimate and show that the solutions to the linearized problem have singularities localized along bicharacteristic curves originating from the boundary. The application to isentropic gas dynamics is detailed.

Paper:

Available as PostScript (462 Kbytes) or gzipped PostScript (168 Kbytes; uncompress using gunzip).

Author(s):

Jean-Francois Coulombel, <jfcoulom@umpa.ens-lyon.fr>

Publishing information:

Comments:

Submitted by:

<jfcoulom@umpa.ens-lyon.fr> July 15 2002.