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

Tom 67 / 1997

Grzegorz Karch Annales Polonici Mathematici 67 (1997), 65-86 DOI: 10.4064/ap-67-1-65-86

Streszczenie

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.

Autorzy

  • Grzegorz Karch

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