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

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Karch G.

Annales Polonici Mathematici

1997

tom 67

nr 1

65-86

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.

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1 Annales Polonici Mathematici

1 Karch G.

1 1997

Wyniki wyszukiwania

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