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L p-convergence rates to nonlinear diffusion waves for quasilinear equations with nonlinear damping

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Abstract

This paper is concerned with the asymptotic behavior of the solution for quasilinear hyperbolic equations with nonlinear damping. The main novelty in this paper is that we obtain the L p(2 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations, and we need none of the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton (Q Appl Math 61:295–313, 2003).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, People’s Republic of China

    Shifeng Geng

  2. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, People’s Republic of China

    Lina Zhang

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  1. Shifeng Geng
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  2. Lina Zhang
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Correspondence to Shifeng Geng.

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Geng, S., Zhang, L. L p-convergence rates to nonlinear diffusion waves for quasilinear equations with nonlinear damping. Z. Angew. Math. Phys. 66, 31–50 (2015). https://doi.org/10.1007/s00033-013-0392-3

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  • DOI: https://doi.org/10.1007/s00033-013-0392-3

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