Degenerate boundary layers for a system of viscous conservation laws

This paper is concerned with existence and asymptotic stability of a boundary layer solution which is a smooth stationary wave for a system of viscous conservation laws in one-dimensional half space. With the aid of the center manifold theory, it is shown that the degenerate boundary layer solution exists under the situation that one characteristic is zero and the other characteristics are negative. Asymptotic stability of the degenerate boundary layer solution is also proved in an algebraically weighted Sobolev space provided that the weight exponent α satisfies α ∈ [1, 5). The stability analysis is based on deriving the a priori estimate by using the weighted energy method combined with the Hardy type inequality with the best possible constant.