A note on the image-stability of boundary layers in viscous conservation laws Original Research Article

We study the initial–boundary value problem for a class of multi-dimensional conservation laws. The semi-group of solutions satisfies a comparison principle and L1L1-contraction property. The first result is concerned with the proof of the L1L1-stability of constant solutions. Next we establish the L1L1-stability of steady solutions to the initial boundary value problem, which are called boundary layer solutions.