### Abstract

We derive a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with a nonlinear dissipation p(u_{t}), where p(v) is a function like. Since our dissipation is weak as |u_{t}| tends to 1 we treat strong solutions rather than usual energy finite solutions.

Original language | English |
---|---|

Pages (from-to) | 681-688 |

Number of pages | 8 |

Journal | Differential and Integral Equations |

Volume | 8 |

Issue number | 3 |

Publication status | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential and Integral Equations*,

*8*(3), 681-688.

**Energy decay for the wave equation with a nonlinear weak dissipation.** / Nakao, Mitsuhiro; Giga, Yoshikazu.

Research output: Contribution to journal › Article

*Differential and Integral Equations*, vol. 8, no. 3, pp. 681-688.

}

TY - JOUR

T1 - Energy decay for the wave equation with a nonlinear weak dissipation

AU - Nakao, Mitsuhiro

AU - Giga, Yoshikazu

PY - 1995

Y1 - 1995

N2 - We derive a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with a nonlinear dissipation p(ut), where p(v) is a function like. Since our dissipation is weak as |ut| tends to 1 we treat strong solutions rather than usual energy finite solutions.

AB - We derive a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with a nonlinear dissipation p(ut), where p(v) is a function like. Since our dissipation is weak as |ut| tends to 1 we treat strong solutions rather than usual energy finite solutions.

UR - http://www.scopus.com/inward/record.url?scp=84972525392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972525392&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 681

EP - 688

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 3

ER -