Ghisi, Marina and Gobbino, Massimo (2010) *Mildly degenerate Kirchhoff equations with weak dissipation: Global existence and time decay.* Journal of Differential Equations, 248/20 (2). pp. 381-402. ISSN 0022-0396

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## Abstract

SUMMARY We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dissipative term tends to zero when t → +∞. We prove that the hyperbolic problem has a unique global solution for suitable values of the parameters. We also prove that the solution decays to zero, as t → +∞, with the same rate of the solution of the limit problem of parabolic type.

Item Type: | Article |
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Uncontrolled Keywords: | singular perturbation, degenerate Kirchhoff equations, quasilinear hyper- bolic equation, weak dissipation, energy estimates. |

Subjects: | Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica |

Divisions: | Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI" |

Depositing User: | dott. Marina Ghisi |

Date Deposited: | 22 Feb 2010 |

Last Modified: | 20 Dec 2010 11:47 |

URI: | http://eprints.adm.unipi.it/id/eprint/671 |

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