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Energy estimate for a linear symmetric hyperbolic-parabolic system in half line

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  • In the present paper, we study the initial boundary value problem for a linear symmetric hyperbolic-parabolic system in one-dimensional half space. We obtain a priori estimates by using an energy method developed by Matsumura--Nishida for half space problem under the assumption that a stability condition of Shizuta--Kawashima type holds. The method developed in the present paper is applicable to showing the nonlinear stability of boundary layer solutions for a system of viscous conservation laws in half space.
    Mathematics Subject Classification: Primary: 35B35, 76N15; Secondary: 35B40.


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