Geodesic
$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
Annales Polonici Mathematici, Tome 67 (1997) no. 1, pp. 65-86.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap-67-1-65-86
Keywords: asymptotic behavior of solutions, dispersive equations, parabolic conservation laws, oscillatory integrals

Grzegorz Karch 1

1 
@article{10_4064_ap_67_1_65_86,
     author = {Grzegorz Karch},
     title = {$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws},
     journal = {Annales Polonici Mathematici},
     pages = {65--86},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {1997},
     doi = {10.4064/ap-67-1-65-86},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-67-1-65-86/}
}
TY  - JOUR
AU  - Grzegorz Karch
TI  - $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
JO  - Annales Polonici Mathematici
PY  - 1997
SP  - 65
EP  - 86
VL  - 67
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-67-1-65-86/
DO  - 10.4064/ap-67-1-65-86
LA  - en
ID  - 10_4064_ap_67_1_65_86
ER  - 
%0 Journal Article
%A Grzegorz Karch
%T $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
%J Annales Polonici Mathematici
%D 1997
%P 65-86
%V 67
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-67-1-65-86/
%R 10.4064/ap-67-1-65-86
%G en
%F 10_4064_ap_67_1_65_86
Grzegorz Karch. $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws. Annales Polonici Mathematici, Tome 67 (1997) no. 1, pp. 65-86. doi : 10.4064/ap-67-1-65-86. http://geodesic.mathdoc.fr/articles/10.4064/ap-67-1-65-86/

Cité par Sources :