$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
Volume 67 / 1997
Annales Polonici Mathematici 67 (1997), 65-86
DOI: 10.4064/ap-67-1-65-86
Abstract
We study the decay in time of the spatial $L^p$-norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
