We study the decay in time of the spatial -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.
@article{bwmeta1.element.bwnjournal-article-apmv67z1p65bwm,
author = {Grzegorz Karch},
title = {$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {65-86},
zbl = {0882.35017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p65bwm}
}
Grzegorz Karch. $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws. Annales Polonici Mathematici, Tome 66 (1997) pp. 65-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p65bwm/
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