### Abstract

Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; u_{tt}−u_{xx}+σ(x,u_{t})+β(x,u)=f(x,t)onI×R^{+}u(x,0)=u_{0}(x),u_{t}(x,0)=u_{1}(x)andu|_{∂I×R+=0} are derived, where I is a bounded interval in R and σ(x, v) is a function such that ∂∂vσ(x,v)≥0andσ(x,v)v≥a(x)|v|^{r+2} with r>-1, a(x)≥ 0 and 1/a(.)εL^{p}(I) for some 0<p<∞.

Original language | English |
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Pages (from-to) | 583-596 |

Number of pages | 14 |

Journal | Studies in Mathematics and its Applications |

Volume | 18 |

Issue number | C |

DOIs | |

Publication status | Published - 1986 Jan 1 |

Externally published | Yes |

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### Keywords

- degenerate dissipative term
- energy decay
- energy method
- nonlinear wave equation

### ASJC Scopus subject areas

- Applied Mathematics