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L p-decay rates to nonlinear diffusion waves for p-system with nonlinear damping

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Abstract

In this paper, we study the L p (2 ⩽ p ⩽ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t), u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (ῡ(x,t), ū(x,t)) governed by the classical Darcys’s law provided that the corresponding prescribed initial error function (w 0(x), z 0(x)) lies in (H 3 × H 2) (ℝ) and |v + − v −| + ∥w 0∥3 + ∥z 0∥2 is sufficiently small. Furthermore, the L p (2 ⩽ p ⩽ +∞) convergence rates of the solutions are also obtained.

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Authors and Affiliations

  1. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan, 430079, China

    Zhu Changjiang & Jiang Mina

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  1. Zhu Changjiang
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  2. Jiang Mina
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Correspondence to Zhu Changjiang.

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Zhu, C., Jiang, M. L p-decay rates to nonlinear diffusion waves for p-system with nonlinear damping. SCI CHINA SER A 49, 721–739 (2006). https://doi.org/10.1007/s11425-006-0721-5

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  • DOI: https://doi.org/10.1007/s11425-006-0721-5

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