Lp-decay rates for perturbations of degenerate scalar viscous shock waves

This contribution shows how to obtain Lp-decay rates, with 2⩽p⩽+∞, for zero-mass perturbations of degenerate scalar viscous shock waves using energy methods. The proof is based upon previous work by Matsumura and Nishihara (Comm. Math. Phys. 165 (1) (1994) 83–96), by extending their weighted energy estimates to Lp-norms, and by obtaining sharp decay rates for the antiderivative of the perturbation with the aid of basic interpolation inequalities. The analysis applies to shocks of all orders of degeneracy and it is elementary.