### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms.** / Nakao, Mitsuhiro.

Research output: Contribution to journal › Article

*Studies in Mathematics and its Applications*, vol. 18, no. C, pp. 583-596. https://doi.org/10.1016/S0168-2024(08)70147-4

}

TY - JOUR

T1 - Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms

AU - Nakao, Mitsuhiro

PY - 1986/1/1

Y1 - 1986/1/1

N2 - Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; utt−uxx+σ(x,ut)+β(x,u)=f(x,t)onI×R+u(x,0)=u0(x),ut(x,0)=u1(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(.)εLp(I) for some 0

AB - Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; utt−uxx+σ(x,ut)+β(x,u)=f(x,t)onI×R+u(x,0)=u0(x),ut(x,0)=u1(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(.)εLp(I) for some 0

KW - degenerate dissipative term

KW - energy decay

KW - energy method

KW - nonlinear wave equation

UR - http://www.scopus.com/inward/record.url?scp=77957035479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957035479&partnerID=8YFLogxK

U2 - 10.1016/S0168-2024(08)70147-4

DO - 10.1016/S0168-2024(08)70147-4

M3 - Article

AN - SCOPUS:77957035479

VL - 18

SP - 583

EP - 596

JO - Studies in Mathematics and its Applications

JF - Studies in Mathematics and its Applications

SN - 0168-2024

IS - C

ER -