Weakly Stable Multi-d Shocks
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
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July 15 2002.
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