### Abstract

We derive a precise decay estimate of the solutions to the initial-boundary value problem for the wave equation with a dissipation: u_{tt} - Δu + a(cursive Greek chi)u_{t} = 0 in Ω × [0, ∞) with the boundary condition u|∂Ω = 0, where a(cursive Greek chi) is a nonnegative function on Ω̄ satisfying a(cursive Greek chi) > 0 a.e. cursive Greek chi ∈ ω and ∫ω1/a(cursive Greek chi)^{p}dcursive Greek chi < ∞ for some 0 < p < 1 for an open set ω ⊂ Ω̄ including a part of ∂Ω with a specific property. The result is applied to prove a global existence and decay of smooth solutions for a semilinear wave equation with such a weak dissipation.

Original language | English |
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Pages (from-to) | 25-42 |

Number of pages | 18 |

Journal | Israel Journal of Mathematics |

Volume | 95 |

Publication status | Published - 1996 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Nakao, M. (1996). Decay of solutions of the wave equation with a local degenerate dissipation.

*Israel Journal of Mathematics*,*95*, 25-42.