### Abstract

The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping U_{tt} + u_{t} -div (a(∇_{u}) ∇_{u}) = 0, and show that, at least when n ≤ 3, they tend, as t → +∞, to those of the nonlinear parabolic equation v_{t} - div (a( ∇_{v}) ∇_{v}) = 0, in the sense that the norm ∥u(.,t) - v(., t)∥L∞(R^{n}) of the difference u - v decays faster than that of either u or v. This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves, first observed by Hsiao, L. and Liu Taiping (see [1, 2]).

Original language | English |
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Pages (from-to) | 63-70 |

Number of pages | 8 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 21 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics