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

Grzegorz Karch

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

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.

Keywords

ENG

asymptotic behavior of solutions, dispersive equations, parabolic conservation laws, oscillatory integrals

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Title

Lp-decay of solutions to dissipative-dispersive perturbations of conservation laws

Affiliations

Abstract

Keywords

Bibliography

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