# ${L}^{p}$-decay of solutions to dissipative-dispersive perturbations of conservation laws

Annales Polonici Mathematici (1997)

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

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topGrzegorz 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 -

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