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ISSN 1088-6850(e) ISSN 0002-9947(p)

Stability of small amplitude boundary layers for mixed hyperbolic-parabolic systems

Author(s): F. Rousset
Journal: Trans. Amer. Math. Soc. 355 (2003), 2991-3008.
MSC (2000): Primary 35K50, 35L50, 35L65, 76H20
Posted: March 17, 2003
MathSciNet review: 1975409
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Abstract: We consider an initial boundary value problem for a symmetrizable mixed hyperbolic-parabolic system of conservation laws with a small viscosity $\varepsilon$ , $u^\varepsilon_t+F(u^\varepsilon)_x =\varepsilon(B(u^\varepsilon) u^\varepsilon_x )_x .$ When the boundary is noncharacteristic for both the viscous and the inviscid system, and the boundary condition dissipative, we show that $u^\varepsilon$ converges to a solution of the inviscid system before the formation of shocks if the amplitude of the boundary layer is sufficiently small. This generalizes previous results obtained for invertible and the linear study of Serre and Zumbrun obtained for a pure Dirichlet's boundary condition.

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