L p -decay of solutions to dissipative-dispersive perturbations of conservation laws

Grzegorz Karch

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 1, page 65-86
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Grzegorz Karch. "$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws." Annales Polonici Mathematici 67.1 (1997): 65-86. <http://eudml.org/doc/270315>.

@article{GrzegorzKarch1997,
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.},
author = {Grzegorz Karch},
journal = {Annales Polonici Mathematici},
keywords = {asymptotic behavior of solutions; dispersive equations; parabolic conservation laws; oscillatory integrals; long time behavior},
language = {eng},
number = {1},
pages = {65-86},
title = {$L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws},
url = {http://eudml.org/doc/270315},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Grzegorz Karch
TI - $L^p$-decay of solutions to dissipative-dispersive perturbations of conservation laws
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 1
SP - 65
EP - 86
AB - 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.
LA - eng
KW - asymptotic behavior of solutions; dispersive equations; parabolic conservation laws; oscillatory integrals; long time behavior
UR - http://eudml.org/doc/270315
ER -

References

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