Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms

Mitsuhiro Nakao

doi:10.1016/S0168-2024(08)70147-4

Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms

Mitsuhiro Nakao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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)=u₀(x),u_t(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(.)εL^p(I) for some 0<p<∞.

Original language	English
Pages (from-to)	583-596
Number of pages	14
Journal	Studies in Mathematics and its Applications
Volume	18
Issue number	C
DOIs	https://doi.org/10.1016/S0168-2024(08)70147-4
Publication status	Published - 1986 Jan 1
Externally published	Yes

Keywords

degenerate dissipative term
energy decay
energy method
nonlinear wave equation

ASJC Scopus subject areas

Applied Mathematics

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10.1016/S0168-2024(08)70147-4

Cite this

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title = "Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms",

abstract = "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",

keywords = "degenerate dissipative term, energy decay, energy method, nonlinear wave equation",

author = "Mitsuhiro Nakao",

year = "1986",

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doi = "10.1016/S0168-2024(08)70147-4",

language = "English",

volume = "18",

pages = "583--596",

journal = "Studies in Mathematics and its Applications",

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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

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JO - Studies in Mathematics and its Applications

JF - Studies in Mathematics and its Applications

IS - C

ER -

Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms

Abstract

Keywords

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